Elliptic curve isogeny class with Cremona label 402930bi (LMFDB label 402930.bi)

• Label: 402930bi
• Number of curves: $2$
• Conductor: $402930$
• CM: no
• Rank: $2$

Elliptic curves in class 402930bi

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
402930.bi2	402930bi1	\([1, -1, 0, -4454214, 3483663948]\)	\(204322939379620803/8705984375000\)	\(416425924404703125000\)	\([]\)	\(28615680\)	\(2.7207\)	\(\Gamma_0(N)\)-optimal^*
402930.bi1	402930bi2	\([1, -1, 0, -357017964, 2596558706198]\)	\(144326645036289953307/12311750\)	\(429306230718065250\)	\([]\)	\(85847040\)	\(3.2700\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 402930bi1.

Rank

The elliptic curves in class 402930bi have rank \(2\).

Complex multiplication

The elliptic curves in class 402930bi do not have complex multiplication.

Modular form 402930.2.a.bi

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.