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SageMath
E = EllipticCurve("ex1")
E.isogeny_class()
Elliptic curves in class 284592.ex
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
284592.ex1 | 284592ex1 | \([0, -1, 0, -461942224, 3961840864192]\) | \(-260607143968297/11270993184\) | \(-471479230641900090799816704\) | \([]\) | \(169344000\) | \(3.8839\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 284592.ex1 has rank \(1\).
Complex multiplication
The elliptic curves in class 284592.ex do not have complex multiplication.Modular form 284592.2.a.ex
sage: E.q_eigenform(10)