Elliptic curve isogeny class with LMFDB label 7650.bm (Cremona label 7650bn)

• Label: 7650.bm
• Number of curves: $2$
• Conductor: $7650$
• CM: no
• Rank: $1$

Elliptic curves in class 7650.bm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7650.bm1	7650bn1	$[1, -1, 1, -3440, 78507]$	$-6667713086715/136$	$-91800$	$[]$	$6048$	$0.48295$	$\Gamma_0(N)$-optimal
7650.bm2	7650bn2	$[1, -1, 1, -3215, 89047]$	$-7466356035/2515456$	$-1237793011200$	$[]$	$18144$	$1.0323$

Rank

The elliptic curves in class 7650.bm have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 - T$
$3$	$1$
$5$	$1$
$17$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$7$	$1 + 2 T + 7 T^{2}$	1.7.c
$11$	$1 + 6 T + 11 T^{2}$	1.11.g
$13$	$1 - 4 T + 13 T^{2}$	1.13.ae
$19$	$1 - 2 T + 19 T^{2}$	1.19.ac
$23$	$1 - 9 T + 23 T^{2}$	1.23.aj
$29$	$1 + 6 T + 29 T^{2}$	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 7650.bm do not have complex multiplication.

Modular form 7650.2.a.bm

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.

$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.