Elliptic curve isogeny class with LMFDB label 464968.l (Cremona label 464968l)

• Label: 464968.l
• Number of curves: $2$
• Conductor: $464968$
• CM: no
• Rank: $1$

Elliptic curves in class 464968.l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
464968.l1	464968l2	\([0, 0, 0, -353419, -80867610]\)	\(50668941906/1127\)	\(108586409752576\)	\([2]\)	\(1824768\)	\(1.8082\)	\(\Gamma_0(N)\)-optimal^*
464968.l2	464968l1	\([0, 0, 0, -21299, -1358082]\)	\(-22180932/3703\)	\(-178391958879232\)	\([2]\)	\(912384\)	\(1.4616\)	\(\Gamma_0(N)\)-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 464968.l1.

Rank

The elliptic curves in class 464968.l have rank \(1\).

Complex multiplication

The elliptic curves in class 464968.l do not have complex multiplication.

Modular form 464968.2.a.l

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.