Elliptic curve isogeny class with LMFDB label 7400.b (Cremona label 7400j)

• Label: 7400.b
• Number of curves: $2$
• Conductor: $7400$
• CM: no
• Rank: $1$

Elliptic curves in class 7400.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7400.b1	7400j1	$[0, 1, 0, -1208, 9088]$	$97556/37$	$74000000000$	$[2]$	$7040$	$0.78504$	$\Gamma_0(N)$-optimal
7400.b2	7400j2	$[0, 1, 0, 3792, 69088]$	$1507142/1369$	$-5476000000000$	$[2]$	$14080$	$1.1316$

Rank

The elliptic curves in class 7400.b have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$5$	$1$
$37$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 + 2 T + 3 T^{2}$	1.3.c
$7$	$1 - 4 T + 7 T^{2}$	1.7.ae
$11$	$1 - 4 T + 11 T^{2}$	1.11.ae
$13$	$1 + 2 T + 13 T^{2}$	1.13.c
$17$	$1 - 2 T + 17 T^{2}$	1.17.ac
$19$	$1 + 4 T + 19 T^{2}$	1.19.e
$23$	$1 + 23 T^{2}$	1.23.a
$29$	$1 + 29 T^{2}$	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 7400.b do not have complex multiplication.

Modular form 7400.2.a.b

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.