Elliptic curve isogeny class with Cremona label 112437g (LMFDB label 112437.a)

• Label: 112437g
• Number of curves: $4$
• Conductor: $112437$
• CM: no
• Rank: $1$

Elliptic curves in class 112437g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
112437.a4	112437g1	\([1, -1, 1, 4144, -219814]\)	\(12167/39\)	\(-25232617154511\)	\([2]\)	\(241920\)	\(1.2548\)	\(\Gamma_0(N)\)-optimal
112437.a3	112437g2	\([1, -1, 1, -39101, -2555044]\)	\(10218313/1521\)	\(984072069025929\)	\([2, 2]\)	\(483840\)	\(1.6014\)
112437.a2	112437g3	\([1, -1, 1, -168836, 24222260]\)	\(822656953/85683\)	\(55436059888460667\)	\([2]\)	\(967680\)	\(1.9479\)
112437.a1	112437g4	\([1, -1, 1, -601286, -179306008]\)	\(37159393753/1053\)	\(681280663171797\)	\([2]\)	\(967680\)	\(1.9479\)

Rank

The elliptic curves in class 112437g have rank \(1\).

Complex multiplication

The elliptic curves in class 112437g do not have complex multiplication.

Modular form 112437.2.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.

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

Isogeny graph

The vertices are labelled with Cremona labels.