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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 1728z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1728.u1 | 1728z1 | \([0, 0, 0, -54, -162]\) | \(-13824\) | \(-1259712\) | \([]\) | \(288\) | \(-0.079872\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1728z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 1728z do not have complex multiplication.Modular form 1728.2.a.z
sage: E.q_eigenform(10)