Elliptic curve isogeny class with Cremona label 374400gm (LMFDB label 374400.gm)

• Label: 374400gm
• Number of curves: $2$
• Conductor: $374400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 374400gm have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 374400gm do not have complex multiplication.

Modular form 374400.2.a.gm

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 Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 374400gm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
374400.gm1	374400gm1	\([0, 0, 0, -259905, -50983450]\)	\(166463915033056/62462907\)	\(728567347248000\)	\([2]\)	\(2981888\)	\(1.8187\)	\(\Gamma_0(N)\)-optimal
374400.gm2	374400gm2	\([0, 0, 0, -221880, -66421600]\)	\(-809134470272/808321761\)	\(-1206817922598912000\)	\([2]\)	\(5963776\)	\(2.1653\)