Elliptic curve isogeny class with Cremona label 417450ei (LMFDB label 417450.ei)

• Label: 417450ei
• Number of curves: $2$
• Conductor: $417450$
• CM: no
• Rank: $0$

Elliptic curves in class 417450ei

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
417450.ei2	417450ei1	\([1, 0, 1, -37876, 5130398]\)	\(-217081801/285660\)	\(-7907251800937500\)	\([2]\)	\(4838400\)	\(1.7434\)	\(\Gamma_0(N)\)-optimal^*
417450.ei1	417450ei2	\([1, 0, 1, -733626, 241685398]\)	\(1577505447721/838350\)	\(23206065067968750\)	\([2]\)	\(9676800\)	\(2.0900\)	\(\Gamma_0(N)\)-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 417450ei1.

Rank

The elliptic curves in class 417450ei have rank \(0\).

Complex multiplication

The elliptic curves in class 417450ei do not have complex multiplication.

Modular form 417450.2.a.ei

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.