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

• Label: 418275bh
• Number of curves: $2$
• Conductor: $418275$
• CM: no
• Rank: $0$

Elliptic curves in class 418275bh

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
418275.bh1	418275bh1	\([0, 0, 1, -35490, -2699564]\)	\(-56197120/3267\)	\(-287393396679675\)	\([]\)	\(1347840\)	\(1.5306\)	\(\Gamma_0(N)\)-optimal^*
418275.bh2	418275bh2	\([0, 0, 1, 192660, -4775729]\)	\(8990228480/5314683\)	\(-467525191198569075\)	\([]\)	\(4043520\)	\(2.0799\)	\(\Gamma_0(N)\)-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 418275bh1.

Rank

The elliptic curves in class 418275bh have rank \(0\).

Complex multiplication

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

Modular form 418275.2.a.bh

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.