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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 858.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
858.e1 | 858f1 | \([1, 1, 1, -572, 118685]\) | \(-20699471212993/6097712265216\) | \(-6097712265216\) | \([]\) | \(2640\) | \(1.1324\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 858.e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 858.e do not have complex multiplication.Modular form 858.2.a.e
sage: E.q_eigenform(10)