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.