Elliptic curve isogeny class with Cremona label 63210h (LMFDB label 63210.k)

• Label: 63210h
• Number of curves: $4$
• Conductor: $63210$
• CM: no
• Rank: $1$

Elliptic curves in class 63210h

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
63210.k3	63210h1	[1, 1, 0, -3357, 73389]	[2]	55296	\(\Gamma_0(N)\)-optimal
63210.k2	63210h2	[1, 1, 0, -4337, 25761]	[2, 2]	110592
63210.k4	63210h3	[1, 1, 0, 16733, 223819]	[2]	221184
63210.k1	63210h4	[1, 1, 0, -41087, -3200889]	[2]	221184

Rank

The elliptic curves in class 63210h have rank \(1\).

Complex multiplication

The elliptic curves in class 63210h do not have complex multiplication.

Modular form 63210.2.a.h

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.