Elliptic curve isogeny class with LMFDB label 310.a (Cremona label 310b)

• Label: 310.a
• Number of curves: $4$
• Conductor: $310$
• CM: no
• Rank: $1$

Elliptic curves in class 310.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
310.a1	310b4	\([1, 0, 0, -2046, 15376]\)	\(947226559343329/443751840500\)	\(443751840500\)	\([2]\)	\(576\)	\(0.92922\)
310.a2	310b2	\([1, 0, 0, -1706, 26980]\)	\(549131937598369/307520\)	\(307520\)	\([6]\)	\(192\)	\(0.37992\)
310.a3	310b1	\([1, 0, 0, -106, 420]\)	\(-131794519969/3174400\)	\(-3174400\)	\([6]\)	\(96\)	\(0.033342\)	\(\Gamma_0(N)\)-optimal
310.a4	310b3	\([1, 0, 0, 454, 1876]\)	\(10347405816671/7447750000\)	\(-7447750000\)	\([2]\)	\(288\)	\(0.58265\)

Rank

The elliptic curves in class 310.a have rank \(1\).

Complex multiplication

The elliptic curves in class 310.a do not have complex multiplication.

Modular form 310.2.a.a

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.