Elliptic curve isogeny class with Cremona label 466578ev (LMFDB label 466578.ev)

• Label: 466578ev
• Number of curves: $4$
• Conductor: $466578$
• CM: no
• Rank: $1$

Elliptic curves in class 466578ev

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
466578.ev4	466578ev1	\([1, -1, 1, 1083505900, -96679310877705]\)	\(11079872671250375/324440155855872\)	\(-4119242748699090744919233543168\)	\([2]\)	\(973209600\)	\(4.5545\)	\(\Gamma_0(N)\)-optimal^*
466578.ev2	466578ev2	\([1, -1, 1, -26127323060, -1548736218835977]\)	\(155355156733986861625/8291568305839392\)	\(105273598235925498010038726486048\)	\([2]\)	\(1946419200\)	\(4.9011\)	\(\Gamma_0(N)\)-optimal^*
466578.ev3	466578ev3	\([1, -1, 1, -9781929275, 2656199514347691]\)	\(-8152944444844179625/235342826399858688\)	\(-2988021715587587235694330849001472\)	\([2]\)	\(2919628800\)	\(5.1038\)	\(\Gamma_0(N)\)-optimal^*
466578.ev1	466578ev4	\([1, -1, 1, -353780557115, 80600647005395115]\)	\(385693937170561837203625/2159357734550274048\)	\(27416207671423248853626348169101312\)	\([2]\)	\(5839257600\)	\(5.4504\)	\(\Gamma_0(N)\)-optimal^*

^*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 4 curves highlighted, and conditionally curve 466578ev1.

Rank

The elliptic curves in class 466578ev have rank \(1\).

Complex multiplication

The elliptic curves in class 466578ev do not have complex multiplication.

Modular form 466578.2.a.ev

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.