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SageMath
E = EllipticCurve("pk1")
E.isogeny_class()
Elliptic curves in class 100800pk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100800.lc1 | 100800pk1 | \([0, 0, 0, -25500, -3715000]\) | \(-6288640/16807\) | \(-4900921200000000\) | \([]\) | \(460800\) | \(1.6982\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 100800pk1 has rank \(1\).
Complex multiplication
The elliptic curves in class 100800pk do not have complex multiplication.Modular form 100800.2.a.pk
sage: E.q_eigenform(10)