Elliptic curve isogeny class with Cremona label 463680s (LMFDB label 463680.s)

• Label: 463680s
• Number of curves: $4$
• Conductor: $463680$
• CM: no
• Rank: $2$

Elliptic curves in class 463680s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
463680.s4	463680s1	\([0, 0, 0, 1257, 24208]\)	\(4707843776/8150625\)	\(-380275560000\)	\([2]\)	\(524288\)	\(0.90693\)	\(\Gamma_0(N)\)-optimal^*
463680.s3	463680s2	\([0, 0, 0, -8868, 251008]\)	\(25829338816/5832225\)	\(17414930534400\)	\([2, 2]\)	\(1048576\)	\(1.2535\)	\(\Gamma_0(N)\)-optimal^*
463680.s1	463680s3	\([0, 0, 0, -133068, 18682288]\)	\(10908552783752/828345\)	\(19787399331840\)	\([2]\)	\(2097152\)	\(1.6001\)	\(\Gamma_0(N)\)-optimal^*
463680.s2	463680s4	\([0, 0, 0, -46668, -3665072]\)	\(470547874952/29383305\)	\(701904628776960\)	\([2]\)	\(2097152\)	\(1.6001\)

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 463680s1.

Rank

The elliptic curves in class 463680s have rank \(2\).

Complex multiplication

The elliptic curves in class 463680s do not have complex multiplication.

Modular form 463680.2.a.s

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.