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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 6378.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6378.e1 | 6378e1 | \([1, 0, 0, -12, -72]\) | \(-192100033/2066472\) | \(-2066472\) | \([]\) | \(1440\) | \(-0.10614\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 6378.e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 6378.e do not have complex multiplication.Modular form 6378.2.a.e
sage: E.q_eigenform(10)