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SageMath
E = EllipticCurve("pm1")
E.isogeny_class()
Elliptic curves in class 187200.pm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 187200.pm1 | 187200bz1 | \([0, 0, 0, 280500, -461810000]\) | \(261568120/10024911\) | \(-93544449523200000000\) | \([]\) | \(4147200\) | \(2.5120\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 187200.pm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 187200.pm do not have complex multiplication.Modular form 187200.2.a.pm
sage: E.q_eigenform(10)