Elliptic curve isogeny class with LMFDB label 7056.s (Cremona label 7056s)

• Label: 7056.s
• Number of curves: $1$
• Conductor: $7056$
• CM: no
• Rank: $1$

Elliptic curves in class 7056.s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7056.s1	7056s1	$[0, 0, 0, -63, 189]$	$48384$	$571536$	$[]$	$672$	$-0.10506$	$\Gamma_0(N)$-optimal

Rank

The elliptic curve 7056.s1 has rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1$
$7$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 + T + 5 T^{2}$	1.5.b
$11$	$1 + T + 11 T^{2}$	1.11.b
$13$	$1 + 2 T + 13 T^{2}$	1.13.c
$17$	$1 - 3 T + 17 T^{2}$	1.17.ad
$19$	$1 - 5 T + 19 T^{2}$	1.19.af
$23$	$1 + 3 T + 23 T^{2}$	1.23.d
$29$	$1 - 6 T + 29 T^{2}$	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 7056.s do not have complex multiplication.

Modular form 7056.2.a.s