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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 472834a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 472834.a1 | 472834a1 | \([1, 1, 0, 2845022462837, 771661314054532925]\) | \(2546717726666099569272885709562552380490951/1731033421687212624949219767930262126592\) | \(-1731033421687212624949219767930262126592\) | \([]\) | \(36180518400\) | \(6.2178\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 472834a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 472834a do not have complex multiplication.Modular form 472834.2.a.a
sage: E.q_eigenform(10)