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SageMath
E = EllipticCurve("ed1")
E.isogeny_class()
Elliptic curves in class 78400.ed
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
78400.ed1 | 78400hw1 | \([0, -1, 0, 1051867, 1301880637]\) | \(12459008/78125\) | \(-807072140000000000000\) | \([]\) | \(2408448\) | \(2.6935\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 78400.ed1 has rank \(1\).
Complex multiplication
The elliptic curves in class 78400.ed do not have complex multiplication.Modular form 78400.2.a.ed
sage: E.q_eigenform(10)