Elliptic curve isogeny class with Cremona label 372400ga (LMFDB label 372400.ga)

• Label: 372400ga
• Number of curves: $2$
• Conductor: $372400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 372400ga have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)
\(19\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 - 4 T + 17 T^{2}\)	1.17.ae
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 372400ga do not have complex multiplication.

Modular form 372400.2.a.ga

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 372400ga

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
372400.ga2	372400ga1	\([0, 0, 0, 6125, 6431250]\)	\(27/19\)	\(-17882648000000000\)	\([2]\)	\(1843200\)	\(1.7976\)	\(\Gamma_0(N)\)-optimal
372400.ga1	372400ga2	\([0, 0, 0, -483875, 126481250]\)	\(13312053/361\)	\(339770312000000000\)	\([2]\)	\(3686400\)	\(2.1442\)