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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 418761e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
418761.e1 | 418761e1 | \([0, 0, 1, -250563, 56333686]\) | \(-98867482624/20696067\) | \(-364173951280778667\) | \([]\) | \(12441600\) | \(2.0914\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 418761e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 418761e do not have complex multiplication.Modular form 418761.2.a.e
sage: E.q_eigenform(10)