Show commands:
SageMath
E = EllipticCurve("pd1")
E.isogeny_class()
Elliptic curves in class 235200.pd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.pd1 | 235200pd1 | \([0, 1, 0, -1143333, 562392963]\) | \(-8780800/2187\) | \(-41167738080000000000\) | \([]\) | \(6289920\) | \(2.4816\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 235200.pd1 has rank \(0\).
Complex multiplication
The elliptic curves in class 235200.pd do not have complex multiplication.Modular form 235200.2.a.pd
sage: E.q_eigenform(10)