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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 10051e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10051.e1 | 10051e1 | \([0, -1, 1, -176, 58753]\) | \(-4096/10051\) | \(-1487908720339\) | \([]\) | \(21120\) | \(1.0147\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 10051e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 10051e do not have complex multiplication.Modular form 10051.2.a.e
sage: E.q_eigenform(10)