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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 116886.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116886.x1 | 116886x1 | \([1, 0, 1, 1100613, -298150778]\) | \(83228502970940543/69854999176704\) | \(-123752392196480914944\) | \([]\) | \(5068800\) | \(2.5431\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 116886.x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 116886.x do not have complex multiplication.Modular form 116886.2.a.x
sage: E.q_eigenform(10)