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SageMath
E = EllipticCurve("pr1")
E.isogeny_class()
Elliptic curves in class 187200.pr
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 187200.pr1 | 187200og1 | \([0, 0, 0, 172500, -304450000]\) | \(304175/21632\) | \(-40370503680000000000\) | \([]\) | \(4838400\) | \(2.4416\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 187200.pr1 has rank \(0\).
Complex multiplication
The elliptic curves in class 187200.pr do not have complex multiplication.Modular form 187200.2.a.pr
sage: E.q_eigenform(10)