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 \(1\).

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.