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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 277350.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277350.z1 | 277350z1 | \([1, 1, 0, -172720675, -4939253637875]\) | \(-1687532377/30233088\) | \(-10209091352936972953608000000\) | \([]\) | \(332881920\) | \(4.0555\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 277350.z1 has rank \(0\).
Complex multiplication
The elliptic curves in class 277350.z do not have complex multiplication.Modular form 277350.2.a.z
sage: E.q_eigenform(10)