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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 5550c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5550.i1 | 5550c1 | \([1, 1, 0, -260, -1680]\) | \(78218787505/2589408\) | \(64735200\) | \([]\) | \(1680\) | \(0.27188\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5550c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 5550c do not have complex multiplication.Modular form 5550.2.a.c
sage: E.q_eigenform(10)