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

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

Elliptic curves in class 7056.bw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7056.bw1	7056ca2	$[0, 0, 0, -1281, 17647]$	$406749952$	$571536$	$[]$	$2160$	$0.34427$
7056.bw2	7056ca1	$[0, 0, 0, -21, 7]$	$1792$	$571536$	$[]$	$720$	$-0.20503$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 7056.bw 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 $\mathbb{F}_p$
$5$	$1 - 3 T + 5 T^{2}$	1.5.ad
$11$	$1 + 3 T + 11 T^{2}$	1.11.d
$13$	$1 + 2 T + 13 T^{2}$	1.13.c
$17$	$1 - 3 T + 17 T^{2}$	1.17.ad
$19$	$1 + T + 19 T^{2}$	1.19.b
$23$	$1 - 3 T + 23 T^{2}$	1.23.ad
$29$	$1 - 6 T + 29 T^{2}$	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 7056.2.a.bw

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.