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

• Label: 7056.a
• Number of curves: $2$
• Conductor: $7056$
• CM: no
• Rank: $0$

Elliptic curves in class 7056.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7056.a1	7056cd2	$[0, 0, 0, -970347, -357821030]$	$838561807/26244$	$3162276680813494272$	$[2]$	$172032$	$2.3249$
7056.a2	7056cd1	$[0, 0, 0, 17493, -18991910]$	$4913/1296$	$-156161811398197248$	$[2]$	$86016$	$1.9783$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 7056.a have rank $0$.

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 + 4 T + 5 T^{2}$	1.5.e
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$13$	$1 - 4 T + 13 T^{2}$	1.13.ae
$17$	$1 + 17 T^{2}$	1.17.a
$19$	$1 + 4 T + 19 T^{2}$	1.19.e
$23$	$1 + 23 T^{2}$	1.23.a
$29$	$1 + 2 T + 29 T^{2}$	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 7056.2.a.a

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.