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SageMath
E = EllipticCurve("pl1")
E.isogeny_class()
Elliptic curves in class 487872pl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 487872.pl1 | 487872pl1 | \([0, 0, 0, 15444, 705672]\) | \(15185664/16807\) | \(-450878477220864\) | \([]\) | \(2580480\) | \(1.4984\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 487872pl1 has rank \(0\).
Complex multiplication
The elliptic curves in class 487872pl do not have complex multiplication.Modular form 487872.2.a.pl
sage: E.q_eigenform(10)