Elliptic curve isogeny class with Cremona label 194810c (LMFDB label 194810.z)

• Label: 194810c
• Number of curves: $2$
• Conductor: $194810$
• CM: no
• Rank: $2$

Elliptic curves in class 194810c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
194810.z2	194810c1	\([1, -1, 1, -107713, 18483281]\)	\(-78013216986489/37918720000\)	\(-67175325521920000\)	\([2]\)	\(1935360\)	\(1.9343\)	\(\Gamma_0(N)\)-optimal
194810.z1	194810c2	\([1, -1, 1, -1888833, 999524177]\)	\(420676324562824569/56350000000\)	\(99827462350000000\)	\([2]\)	\(3870720\)	\(2.2809\)

Rank

The elliptic curves in class 194810c have rank \(2\).

Complex multiplication

The elliptic curves in class 194810c do not have complex multiplication.

Modular form 194810.2.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.