Elliptic curve isogeny class with Cremona label 57960m (LMFDB label 57960.j)

• Label: 57960m
• Number of curves: $2$
• Conductor: $57960$
• CM: no
• Rank: $1$

Elliptic curves in class 57960m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
57960.j1	57960m1	\([0, 0, 0, -363, -362]\)	\(7086244/4025\)	\(3004646400\)	\([2]\)	\(24576\)	\(0.50851\)	\(\Gamma_0(N)\)-optimal
57960.j2	57960m2	\([0, 0, 0, 1437, -2882]\)	\(219804478/129605\)	\(-193499228160\)	\([2]\)	\(49152\)	\(0.85508\)

Rank

The elliptic curves in class 57960m have rank \(1\).

Complex multiplication

The elliptic curves in class 57960m do not have complex multiplication.

Modular form 57960.2.a.m

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.