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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 1728i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1728.g1 | 1728i1 | \([0, 0, 0, 54, 54]\) | \(1536\) | \(-11337408\) | \([]\) | \(288\) | \(0.042505\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1728i1 has rank \(0\).
Complex multiplication
The elliptic curves in class 1728i do not have complex multiplication.Modular form 1728.2.a.i
sage: E.q_eigenform(10)