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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 169338x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 169338.c1 | 169338x1 | \([1, 1, 0, 5067, 60741]\) | \(2979767519/2032056\) | \(-9808346189304\) | \([]\) | \(322560\) | \(1.1815\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 169338x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 169338x do not have complex multiplication.Modular form 169338.2.a.x
sage: E.q_eigenform(10)