Elliptic curve isogeny class with Cremona label 2310c (LMFDB label 2310.c)

• Label: 2310c
• Number of curves: $4$
• Conductor: $2310$
• CM: no
• Rank: $1$

Elliptic curves in class 2310c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2310.c3	2310c1	\([1, 1, 0, -863, -10107]\)	\(71210194441849/165580800\)	\(165580800\)	\([2]\)	\(1536\)	\(0.45766\)	\(\Gamma_0(N)\)-optimal
2310.c2	2310c2	\([1, 1, 0, -1183, -2363]\)	\(183337554283129/104587560000\)	\(104587560000\)	\([2, 2]\)	\(3072\)	\(0.80423\)
2310.c1	2310c3	\([1, 1, 0, -12183, 510237]\)	\(200005594092187129/1027287538200\)	\(1027287538200\)	\([2]\)	\(6144\)	\(1.1508\)
2310.c4	2310c4	\([1, 1, 0, 4697, -12947]\)	\(11456208593737991/6725709375000\)	\(-6725709375000\)	\([2]\)	\(6144\)	\(1.1508\)

Rank

The elliptic curves in class 2310c have rank \(1\).

Complex multiplication

The elliptic curves in class 2310c do not have complex multiplication.

Modular form 2310.2.a.c

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.