Elliptic curve isogeny class with Cremona label 75712z (LMFDB label 75712.bw)

• Label: 75712z
• Number of curves: $4$
• Conductor: $75712$
• CM: no
• Rank: $0$

Elliptic curves in class 75712z

LMFDB label	Cremona label	Weierstrass coefficients	Torsion structure	Modular degree	Optimality
75712.bw4	75712z1	[0, 0, 0, 676, 35152]	[2]	73728	\(\Gamma_0(N)\)-optimal
75712.bw3	75712z2	[0, 0, 0, -12844, 527280]	[2, 2]	147456
75712.bw2	75712z3	[0, 0, 0, -39884, -2425488]	[2]	294912
75712.bw1	75712z4	[0, 0, 0, -202124, 34976240]	[2]	294912

Rank

The elliptic curves in class 75712z have rank \(0\).

Complex multiplication

The elliptic curves in class 75712z do not have complex multiplication.

Modular form 75712.2.a.z

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.