J. E. Cremona
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View article: LuCaNT: LMFDB, Computation, and Number Theory
LuCaNT: LMFDB, Computation, and Number Theory Open
LuCaNT there was a robust panel discussion on this particular review process, as well as on best practices in computational mathematics.Eighty-five registered participants enjoyed the LuCaNT conference, comprising a diverse group from over…
View article: Computing the endomorphism ring of an elliptic curve over a number field
Computing the endomorphism ring of an elliptic curve over a number field Open
We describe deterministic and probabilistic algorithms to determine whether or not a given monic irreducible polynomial is a Hilbert class polynomial, and if so, which one. These algorithms can be used to determine whether a given algebra…
View article: Computing the endomorphism ring of an elliptic curve over a number field
Computing the endomorphism ring of an elliptic curve over a number field Open
We describe deterministic and probabilistic algorithms to determine whether or not a given monic irreducible polynomial H in Z[X] is a Hilbert class polynomial, and if so, which one. These algorithms can be used to determine whether a give…
View article: Local and global densities for Weierstrass models of elliptic curves
Local and global densities for Weierstrass models of elliptic curves Open
We prove local results on the $p$-adic density of elliptic curves over $\mathbb{Q}_p$ with different reduction types, together with global results on densities of elliptic curves over $\mathbb{Q}$ with specified reduction types at one or m…
View article: The density of polynomials of degree n$n$ over Zp${\mathbb {Z}}_p$ having exactly r$r$ roots in Qp${\mathbb {Q}}_p$
The density of polynomials of degree n$n$ over Zp${\mathbb {Z}}_p$ having exactly r$r$ roots in Qp${\mathbb {Q}}_p$ Open
We determine the probability that a random polynomial of degree n over Zp has exactly r roots in Qp, and show that it is given by a rational function of p that is invariant under replacing p by 1/p.
View article: 4. The $L$-Functions and Modular Forms Database by John E. Cremona, John W. Jones, Andrew V. Sutherland, and John Voight
4. The $L$-Functions and Modular Forms Database by John E. Cremona, John W. Jones, Andrew V. Sutherland, and John Voight Open
Calculation, tabulation, and experiment have always played a significant role in number theory.Here we describe the L-functions and modular forms database (LMFDB) [LMFDB],
View article: Global methods for the symplectic type of congruences between elliptic curves
Global methods for the symplectic type of congruences between elliptic curves Open
We describe a systematic investigation into the existence of congruences between the mod p torsion modules of elliptic curves defined over \mathbb{Q} , including methods to determine the symplectic type of such congruences. We classify the…
View article: The density of polynomials of degree n over Zp having exactly r roots in Qp
The density of polynomials of degree n over Zp having exactly r roots in Qp Open
We determine the probability that a random polynomial of degree n over Zp has exactly r roots in Qp, and show that it is given by a rational function of p that is invariant under replacing p by 1/p.
View article: The density of polynomials of degree $n$ over $\mathbb{Z}_p$ having exactly $r$ roots in $\mathbb{Q}_p$
The density of polynomials of degree $n$ over $\mathbb{Z}_p$ having exactly $r$ roots in $\mathbb{Q}_p$ Open
We determine the probability that a random polynomial of degree $n$ over $\mathbb{Z}_p$ has exactly $r$ roots in $\mathbb{Q}_p$, and show that it is given by a rational function of $p$ that is invariant under replacing $p$ by $1/p$.
View article: The density of polynomials of degree $n$ over $\\mathbb{Z}_p$ having\n exactly $r$ roots in $\\mathbb{Q}_p$
The density of polynomials of degree $n$ over $\\mathbb{Z}_p$ having\n exactly $r$ roots in $\\mathbb{Q}_p$ Open
We determine the probability that a random polynomial of degree $n$ over\n$\\mathbb{Z}_p$ has exactly $r$ roots in $\\mathbb{Q}_p$, and show that it is\ngiven by a rational function of $p$ that is invariant under replacing $p$ by\n$1/p$.\n
View article: The proportion of genus one curves over ℚ defined by a binary quartic that everywhere locally have a point
The proportion of genus one curves over ℚ defined by a binary quartic that everywhere locally have a point Open
We consider the proportion of genus one curves over [Formula: see text] of the form [Formula: see text] where [Formula: see text] is a binary quartic form (or more generally of the form [Formula: see text] where also [Formula: see text] is…
View article: sagemath/sage: 9.1
sagemath/sage: 9.1 Open
Mirror of the Sage source tree -- please do not submit PRs here -- everything must be submitted via https://trac.sagemath.org/
View article: Sorting and labelling integral ideals in a number field
Sorting and labelling integral ideals in a number field Open
We define a scheme for labelling and ordering integral ideals of number fields, including prime ideals as a special case. The order we define depends only on the choice of a monic irreducible integral defining polynomial for each field $K$…
View article: The proportion of genus one curves over $\mathbb{Q}$ defined by a binary quartic that everywhere locally have a point
The proportion of genus one curves over $\mathbb{Q}$ defined by a binary quartic that everywhere locally have a point Open
We consider the proportion of genus one curves over $\mathbb{Q}$ of the form $z^2=f(x,y)$ where $f(x,y)\in\mathbb{Z}[x,y]$ is a binary quartic form (or more generally of the form $z^2+h(x,y)z=f(x,y)$ where also $h(x,y)\in\mathbb{Z}[x,y]$ i…
View article: Global methods for the symplectic type of congruences between elliptic\n curves
Global methods for the symplectic type of congruences between elliptic\n curves Open
We describe a systematic investigation into the existence of congruences\nbetween the mod $p$ torsion modules of elliptic curves defined over\n$\\mathbb{Q}$, including methods to determine the symplectic type of such\ncongruences. We class…
View article: On rational Bianchi newforms and abelian surfaces with quaternionic multiplication
On rational Bianchi newforms and abelian surfaces with quaternionic multiplication Open
We study the rational Bianchi newforms (weight 2, trivial character, with rational Hecke eigenvalues) in the LMFDB that are not associated to elliptic curves, but instead to abelian surfaces with quaternionic multiplication. Two of these e…
View article: JohnCremona/eclib v20190226
JohnCremona/eclib v20190226 Open
Changes since last release: fix modular symbol scaling bug introduced in v20170815 checkgens now reads files including torsion points as in ecdata binder support (work in progress)
View article: The symplectic type of congruences between elliptic curves
The symplectic type of congruences between elliptic curves Open
In this talk I will describe a systematic investigation into congruences between the mod $p$ torsion modules of elliptic curves defined over $\mathbb{Q}$. For each such curve $E$ and prime $p$ the $p$-torsion $E[p]$ of $E$, is a 2-dimensio…
View article: Computational Mathematics with SageMath
Computational Mathematics with SageMath Open
Flip to almost any random page in this amazing book, and you will learn how to play with and visualize some beautiful part of mathematics.
View article: Cittadella : the re-discovered treasure
Cittadella : the re-discovered treasure Open
The cranes, excavators and heavy machinery that for more than five years invaded the peacefulness and tranquility of Cittadella are gone and almost completely forgotten. Visitors to Cittadella are struck with awe when they see the bulky ma…
View article: JohnCremona/ecdata: All conductors to 400000
JohnCremona/ecdata: All conductors to 400000 Open
This release extends the range of conductors up to 400,000.
View article: What is the Probability that a Random Integral Quadratic Form in<i>n</i>Variables has an Integral Zero?
What is the Probability that a Random Integral Quadratic Form in<i>n</i>Variables has an Integral Zero? Open
We show that the density of quadratic forms in $n$ variables over $\\mathbb {Z}_p$ that are isotropic is a rational function of $p$, where the rational function is independent of $p$, and we determine this rational function explicitly. Whe…
View article: ecdata: v.2015-09-07
ecdata: v.2015-09-07 Open
No difference in data from previous release, but the repository has been reorganised and split to that branch gh-pages can serve the website at http://johncremona.github.io/ecdata/ .
View article: eclib: v.20150827
eclib: v.20150827 Open
Only change from previous is that the REVISION part of the shared library name was incremented (as it should be for a 100% backward-compatible bugfix). I also made the git tag v20150827.
View article: eclib: bug fix
eclib: bug fix Open
Fixes a bug in mwrank relevant for curves with trivial 2-torsion and non-trivial Sha[2], as reported by William Stein and Jennifer Balakrishnan.
View article: ecdata 2015-05-19
ecdata 2015-05-19 Open
Added data for conductors 350000-359999