Elliptic curve isogeny class with LMFDB label 53312.k (Cremona label 53312ba)

• Label: 53312.k
• Number of curves: $4$
• Conductor: $53312$
• CM: no
• Rank: $1$

Elliptic curves in class 53312.k

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
53312.k1	53312ba4	[0, 1, 0, -354433, 56005599]	[2]	663552
53312.k2	53312ba3	[0, 1, 0, -323073, 70562911]	[2]	331776
53312.k3	53312ba2	[0, 1, 0, -134913, -19114145]	[2]	221184
53312.k4	53312ba1	[0, 1, 0, -9473, -222881]	[2]	110592	\(\Gamma_0(N)\)-optimal

Rank

The elliptic curves in class 53312.k have rank \(1\).

Complex multiplication

The elliptic curves in class 53312.k do not have complex multiplication.

Modular form 53312.2.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.