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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 55545.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
55545.k1 | 55545d1 | \([0, -1, 1, -9887715, -11905786114]\) | \(2580674412544/14467005\) | \(599317544860416151245\) | \([]\) | \(2472960\) | \(2.8291\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 55545.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 55545.k do not have complex multiplication.Modular form 55545.2.a.k
sage: E.q_eigenform(10)