Show commands:
SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 115920.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.bc1 | 115920dr1 | \([0, 0, 0, -218933328, 5078144713052]\) | \(-6218589009063615570313216/56094690913037211867075\) | \(-10468615596954656627481004800\) | \([]\) | \(70726656\) | \(4.0590\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 115920.bc1 has rank \(0\).
Complex multiplication
The elliptic curves in class 115920.bc do not have complex multiplication.Modular form 115920.2.a.bc
sage: E.q_eigenform(10)