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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 169338.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 169338.f1 | 169338ba1 | \([1, 1, 0, -1524, -44208]\) | \(-13719882553/20777472\) | \(-593425377792\) | \([]\) | \(241920\) | \(0.95072\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 169338.f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 169338.f do not have complex multiplication.Modular form 169338.2.a.f
sage: E.q_eigenform(10)