Elliptic curve isogeny class with LMFDB label 418275.ch (Cremona label 418275ch)

• Label: 418275.ch
• Number of curves: $2$
• Conductor: $418275$
• CM: no
• Rank: $1$

Elliptic curves in class 418275.ch

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
418275.ch1	418275ch2	\([1, -1, 0, -495117, -100740834]\)	\(244140625/61347\)	\(3372880836032296875\)	\([2]\)	\(6193152\)	\(2.2651\)	\(\Gamma_0(N)\)-optimal^*
418275.ch2	418275ch1	\([1, -1, 0, 75258, -10051209]\)	\(857375/1287\)	\(-70759737818859375\)	\([2]\)	\(3096576\)	\(1.9186\)	\(\Gamma_0(N)\)-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 418275.ch1.

Rank

The elliptic curves in class 418275.ch have rank \(1\).

Complex multiplication

The elliptic curves in class 418275.ch do not have complex multiplication.

Modular form 418275.2.a.ch

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.