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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 270480.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
270480.f1 | 270480f1 | \([0, -1, 0, -9958006, -5329730069]\) | \(139291573340166716336896/64936748761242890625\) | \(50910411028814426250000\) | \([]\) | \(22619520\) | \(3.0515\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 270480.f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 270480.f do not have complex multiplication.Modular form 270480.2.a.f
sage: E.q_eigenform(10)