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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 75712.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75712.z1 | 75712ct1 | \([0, -1, 0, -225, -4031]\) | \(-1352/7\) | \(-6551207936\) | \([]\) | \(32256\) | \(0.56784\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 75712.z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 75712.z do not have complex multiplication.Modular form 75712.2.a.z
sage: E.q_eigenform(10)