Elliptic curve isogeny class with Cremona label 122694bd (LMFDB label 122694.bj)

• Label: 122694bd
• Number of curves: $4$
• Conductor: $122694$
• CM: no
• Rank: $1$

Elliptic curves in class 122694bd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
122694.bj3	122694bd1	\([1, 0, 1, -112896, -13780934]\)	\(18609625/1188\)	\(10158572055672612\)	\([2]\)	\(1036800\)	\(1.8220\)	\(\Gamma_0(N)\)-optimal
122694.bj4	122694bd2	\([1, 0, 1, 91594, -58114366]\)	\(9938375/176418\)	\(-1508547950267382882\)	\([2]\)	\(2073600\)	\(2.1686\)
122694.bj1	122694bd3	\([1, 0, 1, -1646571, 809986582]\)	\(57736239625/255552\)	\(2185221722198019648\)	\([2]\)	\(3110400\)	\(2.3713\)
122694.bj2	122694bd4	\([1, 0, 1, -828611, 1615186406]\)	\(-7357983625/127552392\)	\(-1090698792092086556808\)	\([2]\)	\(6220800\)	\(2.7179\)

Rank

The elliptic curves in class 122694bd have rank \(1\).

Complex multiplication

The elliptic curves in class 122694bd do not have complex multiplication.

Modular form 122694.2.a.bd

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.