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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 82800.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 82800.bc1 | 82800eo1 | \([0, 0, 0, -255, -470]\) | \(393040/207\) | \(965779200\) | \([]\) | \(27648\) | \(0.41565\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 82800.bc1 has rank \(0\).
Complex multiplication
The elliptic curves in class 82800.bc do not have complex multiplication.Modular form 82800.2.a.bc
sage: E.q_eigenform(10)