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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 5850w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5850.n1 | 5850w1 | \([1, -1, 0, -4992, -135334]\) | \(-48317985/338\) | \(-96250781250\) | \([]\) | \(8400\) | \(0.94095\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5850w1 has rank \(0\).
Complex multiplication
The elliptic curves in class 5850w do not have complex multiplication.Modular form 5850.2.a.w
sage: E.q_eigenform(10)