Elliptic curve isogeny class with LMFDB label 1920.e (Cremona label 1920a)

• Label: 1920.e
• Number of curves: $2$
• Conductor: $1920$
• CM: no
• Rank: $1$

Elliptic curves in class 1920.e

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1920.e1	1920a2	$[0, -1, 0, -41, -39]$	$953312/405$	$3317760$	$[2]$	$256$	$-0.052094$
1920.e2	1920a1	$[0, -1, 0, 9, -9]$	$281216/225$	$-57600$	$[2]$	$128$	$-0.39867$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 1920.e have rank $1$.

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$7$	$1 - 2 T + 7 T^{2}$	1.7.ac
$11$	$1 + 2 T + 11 T^{2}$	1.11.c
$13$	$1 + 2 T + 13 T^{2}$	1.13.c
$17$	$1 + 2 T + 17 T^{2}$	1.17.c
$19$	$1 - 2 T + 19 T^{2}$	1.19.ac
$23$	$1 - 2 T + 23 T^{2}$	1.23.ac
$29$	$1 + 6 T + 29 T^{2}$	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1920.e do not have complex multiplication.

Modular form 1920.2.a.e

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.