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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 648.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
648.d1 | 648c1 | \([0, 0, 0, -27, -378]\) | \(-36\) | \(-60466176\) | \([]\) | \(144\) | \(0.17365\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 648.d1 has rank \(0\).
Complex multiplication
The elliptic curves in class 648.d do not have complex multiplication.Modular form 648.2.a.d
sage: E.q_eigenform(10)