Elliptic curve isogeny class with Cremona label 470890ci (LMFDB label 470890.ci)

• Label: 470890ci
• Number of curves: $2$
• Conductor: $470890$
• CM: no
• Rank: $1$

Elliptic curves in class 470890ci

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
470890.ci2	470890ci1	\([1, 0, 0, -3344300, 2768044432]\)	\(-115501303/25600\)	\(-916837753705660595200\)	\([2]\)	\(33868800\)	\(2.7428\)	\(\Gamma_0(N)\)-optimal^*
470890.ci1	470890ci2	\([1, 0, 0, -56083980, 161651604400]\)	\(544737993463/20000\)	\(716279495082547340000\)	\([2]\)	\(67737600\)	\(3.0893\)	\(\Gamma_0(N)\)-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 470890ci1.

Rank

The elliptic curves in class 470890ci have rank \(1\).

Complex multiplication

The elliptic curves in class 470890ci do not have complex multiplication.

Modular form 470890.2.a.ci

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.