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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 128576u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
128576.bb1 | 128576u1 | \([0, -1, 0, -65921, -669311]\) | \(1027243729/587776\) | \(18127587540729856\) | \([]\) | \(811008\) | \(1.8094\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 128576u1 has rank \(2\).
Complex multiplication
The elliptic curves in class 128576u do not have complex multiplication.Modular form 128576.2.a.u
sage: E.q_eigenform(10)