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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 102550bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102550.ba1 | 102550bc1 | \([1, 0, 0, -5509888, 9989165392]\) | \(-47357851934411832865/82956466370366288\) | \(-32404869675924331250000\) | \([]\) | \(6432000\) | \(3.0098\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 102550bc1 has rank \(1\).
Complex multiplication
The elliptic curves in class 102550bc do not have complex multiplication.Modular form 102550.2.a.bc
sage: E.q_eigenform(10)