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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 51600bn
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51600.x1 | 51600bn1 | \([0, -1, 0, -6712133, -6795441363]\) | \(-522547125460258816/9506987907075\) | \(-608447226052800000000\) | \([]\) | \(2580480\) | \(2.7841\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 51600bn1 has rank \(0\).
Complex multiplication
The elliptic curves in class 51600bn do not have complex multiplication.Modular form 51600.2.a.bn
sage: E.q_eigenform(10)