Elliptic curve isogeny class with Cremona label 485100ge (LMFDB label 485100.ge)

• Label: 485100ge
• Number of curves: $2$
• Conductor: $485100$
• CM: no
• Rank: $1$

Elliptic curves in class 485100ge

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
485100.ge2	485100ge1	\([0, 0, 0, -907592700, -14447224355375]\)	\(-3856034557002072064/1973796785296875\)	\(-42321223479295700542968750000\)	\([2]\)	\(371589120\)	\(4.1976\)	\(\Gamma_0(N)\)-optimal^*
485100.ge1	485100ge2	\([0, 0, 0, -15977389575, -777235132777250]\)	\(1314817350433665559504/190690249278375\)	\(65419051972517091733500000000\)	\([2]\)	\(743178240\)	\(4.5442\)	\(\Gamma_0(N)\)-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 485100ge1.

Rank

The elliptic curves in class 485100ge have rank \(1\).

Complex multiplication

The elliptic curves in class 485100ge do not have complex multiplication.

Modular form 485100.2.a.ge

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.