Elliptic curve isogeny class with Cremona label 464607j (LMFDB label 464607.j)

• Label: 464607j
• Number of curves: $2$
• Conductor: $464607$
• CM: no
• Rank: $1$

Elliptic curves in class 464607j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
464607.j2	464607j1	\([1, -1, 1, 6430, 248960]\)	\(857375/1287\)	\(-44139527609463\)	\([2]\)	\(774144\)	\(1.3036\)	\(\Gamma_0(N)\)-optimal^*
464607.j1	464607j2	\([1, -1, 1, -42305, 2529758]\)	\(244140625/61347\)	\(2103984149384403\)	\([2]\)	\(1548288\)	\(1.6502\)	\(\Gamma_0(N)\)-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 464607j1.

Rank

The elliptic curves in class 464607j have rank \(1\).

Complex multiplication

The elliptic curves in class 464607j do not have complex multiplication.

Modular form 464607.2.a.j

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.