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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 42483u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 42483.f1 | 42483u1 | \([1, 0, 0, -7647235, 6884920454]\) | \(7253758561/1193859\) | \(8140048005874731428979\) | \([]\) | \(2177280\) | \(2.9258\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 42483u1 has rank \(1\).
Complex multiplication
The elliptic curves in class 42483u do not have complex multiplication.Modular form 42483.2.a.u
sage: E.q_eigenform(10)