Elliptic curve isogeny class with Cremona label 488410c (LMFDB label 488410.c)

• Label: 488410c
• Number of curves: $2$
• Conductor: $488410$
• CM: no
• Rank: $1$

Elliptic curves in class 488410c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
488410.c2	488410c1	\([1, 0, 1, -162418841719, 21703174151790042]\)	\(827813553991775477153/123566310400000000\)	\(70729483292707070623463859200000000\)	\([2]\)	\(4211343360\)	\(5.4114\)	\(\Gamma_0(N)\)-optimal^*
488410.c1	488410c2	\([1, 0, 1, -2497346853239, 1518992573020672986]\)	\(3009261308803109129809313/85820312500000000\)	\(49123635232728044389882812500000000\)	\([2]\)	\(8422686720\)	\(5.7580\)	\(\Gamma_0(N)\)-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 488410c1.

Rank

The elliptic curves in class 488410c have rank \(1\).

Complex multiplication

The elliptic curves in class 488410c do not have complex multiplication.

Modular form 488410.2.a.c

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.