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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 169065.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
169065.e1 | 169065a1 | \([0, 0, 1, -123267, 16658032]\) | \(-57834888040448/823875\) | \(-2950771750875\) | \([]\) | \(1188864\) | \(1.5324\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 169065.e1 has rank \(2\).
Complex multiplication
The elliptic curves in class 169065.e do not have complex multiplication.Modular form 169065.2.a.e
sage: E.q_eigenform(10)