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

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

Elliptic curves in class 7056.n

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
7056.n1	7056bv2	$[0, 0, 0, -19551, -974806]$	$109744/9$	$67778563974912$	$[2]$	$21504$	$1.3965$
7056.n2	7056bv1	$[0, 0, 0, -4116, 84035]$	$16384/3$	$1412053416144$	$[2]$	$10752$	$1.0499$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 7056.n 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 $\mathbb{F}_p$
$5$	$1 + 2 T + 5 T^{2}$	1.5.c
$11$	$1 - 2 T + 11 T^{2}$	1.11.ac
$13$	$1 + 4 T + 13 T^{2}$	1.13.e
$17$	$1 + 6 T + 17 T^{2}$	1.17.g
$19$	$1 + 8 T + 19 T^{2}$	1.19.i
$23$	$1 + 6 T + 23 T^{2}$	1.23.g
$29$	$1 - 10 T + 29 T^{2}$	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 7056.2.a.n

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.