Elliptic curve isogeny class with Cremona label 31713b (LMFDB label 31713.a)

• Label: 31713b
• Number of curves: $2$
• Conductor: $31713$
• CM: no
• Rank: $2$

Elliptic curves in class 31713b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
31713.a2	31713b1	\([1, 1, 1, 11, 50]\)	\(4913/33\)	\(-983103\)	\([2]\)	\(3584\)	\(-0.16842\)	\(\Gamma_0(N)\)-optimal
31713.a1	31713b2	\([1, 1, 1, -144, 546]\)	\(11089567/1089\)	\(32442399\)	\([2]\)	\(7168\)	\(0.17816\)

Rank

The elliptic curves in class 31713b have rank \(2\).

Complex multiplication

The elliptic curves in class 31713b do not have complex multiplication.

Modular form 31713.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.