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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 161700.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 161700.u1 | 161700ec1 | \([0, -1, 0, -856036533, 9634522427937]\) | \(61398847532302336/44027317125\) | \(49746509470745356500000000\) | \([]\) | \(60963840\) | \(3.8660\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 161700.u1 has rank \(1\).
Complex multiplication
The elliptic curves in class 161700.u do not have complex multiplication.Modular form 161700.2.a.u
sage: E.q_eigenform(10)