Elliptic curve isogeny class with Cremona label 82810ca (LMFDB label 82810.cn)

• Label: 82810ca
• Number of curves: $4$
• Conductor: $82810$
• CM: no
• Rank: $1$

Elliptic curves in class 82810ca

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
82810.cn4	82810ca1	\([1, 1, 1, -1933786, -1034486237]\)	\(1408317602329/2153060\)	\(1222656571799395460\)	\([2]\)	\(2322432\)	\(2.3703\)	\(\Gamma_0(N)\)-optimal
82810.cn3	82810ca2	\([1, 1, 1, -2513456, -363923981]\)	\(3092354182009/1689383150\)	\(959348745801168509150\)	\([2]\)	\(4644864\)	\(2.7168\)
82810.cn2	82810ca3	\([1, 1, 1, -7854701, 7460627299]\)	\(94376601570889/12235496000\)	\(6948161961870647336000\)	\([2]\)	\(6967296\)	\(2.9196\)
82810.cn1	82810ca4	\([1, 1, 1, -121470021, 515230215443]\)	\(349046010201856969/7245875000\)	\(4114709616632580875000\)	\([2]\)	\(13934592\)	\(3.2661\)

Rank

The elliptic curves in class 82810ca have rank \(1\).

Complex multiplication

The elliptic curves in class 82810ca do not have complex multiplication.

Modular form 82810.2.a.ca

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.