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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 5775.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5775.w1 | 5775e1 | \([0, -1, 1, -7708, -222807]\) | \(5186867200/754677\) | \(7369892578125\) | \([]\) | \(20160\) | \(1.1942\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5775.w1 has rank \(0\).
Complex multiplication
The elliptic curves in class 5775.w do not have complex multiplication.Modular form 5775.2.a.w
sage: E.q_eigenform(10)