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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 212160u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 212160.hd1 | 212160u1 | \([0, 1, 0, -15425, -773697]\) | \(-1548415333009/77332320\) | \(-20272203694080\) | \([]\) | \(430080\) | \(1.3144\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 212160u1 has rank \(1\).
Complex multiplication
The elliptic curves in class 212160u do not have complex multiplication.Modular form 212160.2.a.u
sage: E.q_eigenform(10)