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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 289800.bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 289800.bt1 | 289800bt1 | \([0, 0, 0, -781500, -662037500]\) | \(-144814859264/435654247\) | \(-158795973031500000000\) | \([]\) | \(7795200\) | \(2.5630\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 289800.bt1 has rank \(0\).
Complex multiplication
The elliptic curves in class 289800.bt do not have complex multiplication.Modular form 289800.2.a.bt
sage: E.q_eigenform(10)