Elliptic curve isogeny class with Cremona label 92400gc (LMFDB label 92400.fa)

• Label: 92400gc
• Number of curves: $4$
• Conductor: $92400$
• CM: no
• Rank: $1$

Elliptic curves in class 92400gc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
92400.fa4	92400gc1	\([0, 1, 0, 102592, -16804812]\)	\(1865864036231/2993760000\)	\(-191600640000000000\)	\([2]\)	\(737280\)	\(2.0013\)	\(\Gamma_0(N)\)-optimal
92400.fa3	92400gc2	\([0, 1, 0, -697408, -172004812]\)	\(586145095611769/140040608400\)	\(8962598937600000000\)	\([2, 2]\)	\(1474560\)	\(2.3479\)
92400.fa2	92400gc3	\([0, 1, 0, -3777408, 2680075188]\)	\(93137706732176569/5369647977540\)	\(343657470562560000000\)	\([4]\)	\(2949120\)	\(2.6945\)
92400.fa1	92400gc4	\([0, 1, 0, -10417408, -12944084812]\)	\(1953542217204454969/170843779260\)	\(10934001872640000000\)	\([2]\)	\(2949120\)	\(2.6945\)

Rank

The elliptic curves in class 92400gc have rank \(1\).

Complex multiplication

The elliptic curves in class 92400gc do not have complex multiplication.

Modular form 92400.2.a.gc

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.