Elliptic curve isogeny class with LMFDB label 302379.bi (Cremona label 302379bi)

• Label: 302379.bi
• Number of curves: $4$
• Conductor: $302379$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 302379.bi have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 + T\)
\(7\)	\(1\)
\(11\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 - T + 2 T^{2}\)	1.2.ab
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 302379.bi do not have complex multiplication.

Modular form 302379.2.a.bi

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 302379.bi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
302379.bi1	302379bi4	\([1, 1, 0, -1079201, -430427136]\)	\(666940371553/2756193\)	\(574452305044641177\)	\([2]\)	\(5898240\)	\(2.2630\)
302379.bi2	302379bi2	\([1, 1, 0, -100916, 605235]\)	\(545338513/314721\)	\(65594899883990169\)	\([2, 2]\)	\(2949120\)	\(1.9164\)
302379.bi3	302379bi1	\([1, 1, 0, -71271, 7275360]\)	\(192100033/561\)	\(116924955229929\)	\([2]\)	\(1474560\)	\(1.5698\)	\(\Gamma_0(N)\)-optimal
302379.bi4	302379bi3	\([1, 1, 0, 403049, 5342506]\)	\(34741712447/20160657\)	\(-4201932116097958473\)	\([2]\)	\(5898240\)	\(2.2630\)