Elliptic curve isogeny class with LMFDB label 7650.bk (Cremona label 7650cp)

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

Elliptic curves in class 7650.bk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7650.bk1	7650cp2	$[1, -1, 1, -366305, -1824303]$	$19088138515945/11040808032$	$3144042599737500000$	$[]$	$144000$	$2.2388$
7650.bk2	7650cp1	$[1, -1, 1, -248630, 47779647]$	$3730569358698025/102$	$46473750$	$[]$	$28800$	$1.4341$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 7650.bk 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 $\mathbb{F}_p$
$7$	$1 + 3 T + 7 T^{2}$	1.7.d
$11$	$1 - 3 T + 11 T^{2}$	1.11.ad
$13$	$1 + 4 T + 13 T^{2}$	1.13.e
$19$	$1 + 5 T + 19 T^{2}$	1.19.f
$23$	$1 - 4 T + 23 T^{2}$	1.23.ae
$29$	$1 + 29 T^{2}$	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 7650.2.a.bk

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.

$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.