Elliptic curve isogeny class with LMFDB label 10780.k (Cremona label 10780f)

• Label: 10780.k
• Number of curves: $4$
• Conductor: $10780$
• CM: no
• Rank: $1$

Elliptic curves in class 10780.k

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
10780.k1	10780f4	[0, -1, 0, -347916, 79103816]	[2]	62208
10780.k2	10780f3	[0, -1, 0, -21821, 1232330]	[2]	31104
10780.k3	10780f2	[0, -1, 0, -4916, 76616]	[2]	20736
10780.k4	10780f1	[0, -1, 0, -2221, -38730]	[2]	10368	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 10780.k have rank \(1\).

Complex multiplication

The elliptic curves in class 10780.k do not have complex multiplication.

Modular form 10780.2.a.k

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 LMFDB 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 LMFDB labels.