Elliptic curve isogeny class with Cremona label 422370et (LMFDB label 422370.et)

• Label: 422370et
• Number of curves: $4$
• Conductor: $422370$
• CM: no
• Rank: $0$

Elliptic curves in class 422370et

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
422370.et3	422370et1	\([1, -1, 1, -89957, -10476711]\)	\(-63378025803/812500\)	\(-1032069014437500\)	\([2]\)	\(3981312\)	\(1.6901\)	\(\Gamma_0(N)\)-optimal^*
422370.et2	422370et2	\([1, -1, 1, -1443707, -667316211]\)	\(261984288445803/42250\)	\(53667588750750\)	\([2]\)	\(7962624\)	\(2.0367\)	\(\Gamma_0(N)\)-optimal^*
422370.et4	422370et3	\([1, -1, 1, 316168, -53489861]\)	\(3774555693/3515200\)	\(-3255089526981489600\)	\([2]\)	\(11943936\)	\(2.2395\)	\(\Gamma_0(N)\)-optimal^*
422370.et1	422370et4	\([1, -1, 1, -1633232, -480798341]\)	\(520300455507/193072360\)	\(178785792269458316280\)	\([2]\)	\(23887872\)	\(2.5860\)	\(\Gamma_0(N)\)-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 422370et1.

Rank

The elliptic curves in class 422370et have rank \(0\).

Complex multiplication

The elliptic curves in class 422370et do not have complex multiplication.

Modular form 422370.2.a.et

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.