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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 180336.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 180336.p1 | 180336bg1 | \([0, -1, 0, -99145036008, -12170496618713232]\) | \(-3772118414306118217515625/56562751486929272832\) | \(-1616150669592087302957232713367552\) | \([]\) | \(1091171520\) | \(5.1754\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 180336.p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 180336.p do not have complex multiplication.Modular form 180336.2.a.p
sage: E.q_eigenform(10)