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SageMath
E = EllipticCurve("ex1")
E.isogeny_class()
Elliptic curves in class 426888ex
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 426888.ex1 | 426888ex1 | \([0, 0, 0, 2116653, -2678022578]\) | \(68782/243\) | \(-3705136269139308681216\) | \([]\) | \(18144000\) | \(2.8216\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 426888ex1 has rank \(1\).
Complex multiplication
The elliptic curves in class 426888ex do not have complex multiplication.Modular form 426888.2.a.ex
sage: E.q_eigenform(10)