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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 84640.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 84640.w1 | 84640s1 | \([0, -1, 0, 52195, -1155078475]\) | \(25934336/950546875\) | \(-576368851668160000000\) | \([]\) | \(2128896\) | \(2.6625\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 84640.w1 has rank \(0\).
Complex multiplication
The elliptic curves in class 84640.w do not have complex multiplication.Modular form 84640.2.a.w
sage: E.q_eigenform(10)