Elliptic curve isogeny class with Cremona label 57b (LMFDB label 57.c)

• Label: 57b
• Number of curves: $4$
• Conductor: $57$
• CM: no
• Rank: $0$

Elliptic curves in class 57b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
57.c2	57b1	$[1, 0, 1, -7, 5]$	$30664297/3249$	$3249$	$[2, 2]$	$3$	$-0.59158$	$\Gamma_0(N)$-optimal
57.c3	57b2	$[1, 0, 1, -2, -1]$	$389017/57$	$57$	$[2]$	$6$	$-0.93816$
57.c1	57b3	$[1, 0, 1, -102, 385]$	$115714886617/1539$	$1539$	$[4]$	$6$	$-0.24501$
57.c4	57b4	$[1, 0, 1, 8, 29]$	$67419143/390963$	$-390963$	$[2]$	$6$	$-0.24501$

Rank

The elliptic curves in class 57b have rank $0$.

Complex multiplication

The elliptic curves in class 57b do not have complex multiplication.

Modular form 57.2.a.b

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 Cremona numbering.

$\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.