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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 10584.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10584.u1 | 10584e1 | \([0, 0, 0, -17786412, -28446198732]\) | \(116634423954432/1977326743\) | \(10549708201290690157824\) | \([]\) | \(760320\) | \(3.0236\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 10584.u1 has rank \(0\).
Complex multiplication
The elliptic curves in class 10584.u do not have complex multiplication.Modular form 10584.2.a.u
sage: E.q_eigenform(10)