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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 80688be
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
80688.w1 | 80688be1 | \([0, 1, 0, -12244964, -16489989960]\) | \(59090512/27\) | \(92777421151773395712\) | \([]\) | \(4959360\) | \(2.7885\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 80688be1 has rank \(1\).
Complex multiplication
The elliptic curves in class 80688be do not have complex multiplication.Modular form 80688.2.a.be
sage: E.q_eigenform(10)