Elliptic curve isogeny class with Cremona label 418800bv (LMFDB label 418800.bv)

• Label: 418800bv
• Number of curves: $2$
• Conductor: $418800$
• CM: no
• Rank: $1$

Elliptic curves in class 418800bv

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
418800.bv1	418800bv1	\([0, 1, 0, -18174008, -29846148012]\)	\(-10372797669976737841/7632630000000\)	\(-488488320000000000000\)	\([]\)	\(22353408\)	\(2.9039\)	\(\Gamma_0(N)\)-optimal^*
418800.bv2	418800bv2	\([0, 1, 0, 72965992, 1656909971988]\)	\(671282315177095816559/18919046447754148470\)	\(-1210818972656265502080000000\)	\([]\)	\(156473856\)	\(3.8768\)	\(\Gamma_0(N)\)-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 418800bv1.

Rank

The elliptic curves in class 418800bv have rank \(1\).

Complex multiplication

The elliptic curves in class 418800bv do not have complex multiplication.

Modular form 418800.2.a.bv

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.