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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 81144.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 81144.bg1 | 81144bo1 | \([0, 0, 0, 10771425, -344654606961]\) | \(100718081964000000/37453512751940327\) | \(-51395880104927313124185072\) | \([]\) | \(16450560\) | \(3.6126\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 81144.bg1 has rank \(0\).
Complex multiplication
The elliptic curves in class 81144.bg do not have complex multiplication.Modular form 81144.2.a.bg
sage: E.q_eigenform(10)