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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 338100.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 338100.x1 | 338100x1 | \([0, -1, 0, -16494333, 25790286537]\) | \(-20256384340484096/718449183\) | \(-17602004983500000000\) | \([]\) | \(13392000\) | \(2.7824\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 338100.x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 338100.x do not have complex multiplication.Modular form 338100.2.a.x
sage: E.q_eigenform(10)