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SageMath
E = EllipticCurve("ex1")
E.isogeny_class()
Elliptic curves in class 397488ex
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
397488.ex1 | 397488ex1 | \([0, -1, 0, -568416, 115728768]\) | \(249395415529/73513818\) | \(5986925741613293568\) | \([]\) | \(11612160\) | \(2.3088\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 397488ex1 has rank \(1\).
Complex multiplication
The elliptic curves in class 397488ex do not have complex multiplication.Modular form 397488.2.a.ex
sage: E.q_eigenform(10)