Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 388815.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388815.f1 | 388815f1 | \([0, -1, 1, -19640980, -33497256822]\) | \(-243808749105152/820125\) | \(-2818668220302382875\) | \([]\) | \(25062912\) | \(2.7617\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 388815.f1 has rank \(0\).
Complex multiplication
The elliptic curves in class 388815.f do not have complex multiplication.Modular form 388815.2.a.f
sage: E.q_eigenform(10)