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

• Label: 470890.dg
• Number of curves: $2$
• Conductor: $470890$
• CM: no
• Rank: $0$

Elliptic curves in class 470890.dg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
470890.dg1	470890dg2	\([1, 1, 1, -1144571, -471778007]\)	\(544737993463/20000\)	\(6088275251660000\)	\([2]\)	\(9676800\)	\(2.1164\)	\(\Gamma_0(N)\)-optimal^*
470890.dg2	470890dg1	\([1, 1, 1, -68251, -8099351]\)	\(-115501303/25600\)	\(-7792992322124800\)	\([2]\)	\(4838400\)	\(1.7698\)	\(\Gamma_0(N)\)-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 470890.dg1.

Rank

The elliptic curves in class 470890.dg have rank \(0\).

Complex multiplication

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

Modular form 470890.2.a.dg

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.