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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 1215.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1215.a1 | 1215c1 | \([0, 0, 1, 27, -16]\) | \(995328/625\) | \(-1366875\) | \([]\) | \(216\) | \(-0.13361\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1215.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 1215.a do not have complex multiplication.Modular form 1215.2.a.a
sage: E.q_eigenform(10)