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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 73689f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
73689.k1 | 73689f1 | \([0, -1, 1, -161, -100]\) | \(31719424/17661\) | \(258574701\) | \([]\) | \(17472\) | \(0.30457\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 73689f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 73689f do not have complex multiplication.Modular form 73689.2.a.f
sage: E.q_eigenform(10)