Elliptic curve isogeny class with LMFDB label 62400.ei (Cremona label 62400de)

• Label: 62400.ei
• Number of curves: $4$
• Conductor: $62400$
• CM: no
• Rank: $1$

Elliptic curves in class 62400.ei

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
62400.ei1	62400de4	\([0, 1, 0, -56160033, -162009071937]\)	\(19129597231400697604/26325\)	\(26956800000000\)	\([2]\)	\(2359296\)	\(2.7434\)
62400.ei2	62400de2	\([0, 1, 0, -3510033, -2532221937]\)	\(18681746265374416/693005625\)	\(177409440000000000\)	\([2, 2]\)	\(1179648\)	\(2.3968\)
62400.ei3	62400de3	\([0, 1, 0, -3348033, -2776355937]\)	\(-4053153720264484/903687890625\)	\(-925376400000000000000\)	\([2]\)	\(2359296\)	\(2.7434\)
62400.ei4	62400de1	\([0, 1, 0, -229533, -35761437]\)	\(83587439220736/13990184325\)	\(223842949200000000\)	\([2]\)	\(589824\)	\(2.0502\)	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 62400.ei have rank \(1\).

Complex multiplication

The elliptic curves in class 62400.ei do not have complex multiplication.

Modular form 62400.2.a.ei

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 LMFDB 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 LMFDB labels.