Elliptic curve isogeny class with Cremona label 51714g (LMFDB label 51714.g)

• Label: 51714g
• Number of curves: $2$
• Conductor: $51714$
• CM: no
• Rank: $1$

Elliptic curves in class 51714g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
51714.g1	51714g1	\([1, -1, 0, -29067102, 58309856788]\)	\(771864882375147625/29358565696512\)	\(103305269876510219461632\)	\([2]\)	\(4300800\)	\(3.1842\)	\(\Gamma_0(N)\)-optimal
51714.g2	51714g2	\([1, -1, 0, 12060738, 210063360820]\)	\(55138849409108375/5449537181735712\)	\(-19175524958570059750892832\)	\([2]\)	\(8601600\)	\(3.5307\)

Rank

The elliptic curves in class 51714g have rank \(1\).

Complex multiplication

The elliptic curves in class 51714g do not have complex multiplication.

Modular form 51714.2.a.g

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.