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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 250470u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 250470.u1 | 250470u1 | \([1, -1, 0, -1835871615, 30303357239821]\) | \(-529867148566940437900681/526595228427755520\) | \(-680080870142684484642938880\) | \([]\) | \(167731200\) | \(4.0685\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 250470u1 has rank \(0\).
Complex multiplication
The elliptic curves in class 250470u do not have complex multiplication.Modular form 250470.2.a.u
sage: E.q_eigenform(10)