Elliptic curve isogeny class with LMFDB label 77760.dg (Cremona label 77760er)

• Label: 77760.dg
• Number of curves: $2$
• Conductor: $77760$
• CM: no
• Rank: $0$

Elliptic curves in class 77760.dg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
77760.dg1	77760er1	$[0, 0, 0, -9612, -362736]$	$-171307467/10$	$-5733089280$	$[]$	$62208$	$0.93516$	$\Gamma_0(N)$-optimal
77760.dg2	77760er2	$[0, 0, 0, -972, -983664]$	$-243/1000$	$-417942208512000$	$[]$	$186624$	$1.4845$

Rank

The elliptic curves in class 77760.dg have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1$
$5$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$7$	$1 + 2 T + 7 T^{2}$	1.7.c
$11$	$1 + 11 T^{2}$	1.11.a
$13$	$1 - T + 13 T^{2}$	1.13.ab
$17$	$1 + 3 T + 17 T^{2}$	1.17.d
$19$	$1 - 2 T + 19 T^{2}$	1.19.ac
$23$	$1 + 23 T^{2}$	1.23.a
$29$	$1 + 3 T + 29 T^{2}$	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 77760.dg do not have complex multiplication.

Modular form 77760.2.a.dg

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.