Elliptic curve isogeny class with Cremona label 476850ds (LMFDB label 476850.ds)

• Label: 476850ds
• Number of curves: $2$
• Conductor: $476850$
• CM: no
• Rank: $1$

Elliptic curves in class 476850ds

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
476850.ds2	476850ds1	\([1, 0, 1, -86851, 7977098]\)	\(192100033/38148\)	\(14387499722062500\)	\([2]\)	\(3538944\)	\(1.8167\)	\(\Gamma_0(N)\)-optimal^*
476850.ds1	476850ds2	\([1, 0, 1, -1315101, 580341598]\)	\(666940371553/37026\)	\(13964337965531250\)	\([2]\)	\(7077888\)	\(2.1633\)	\(\Gamma_0(N)\)-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 476850ds1.

Rank

The elliptic curves in class 476850ds have rank \(1\).

Complex multiplication

The elliptic curves in class 476850ds do not have complex multiplication.

Modular form 476850.2.a.ds

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.