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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 493680.bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 493680.bt1 | 493680bt1 | \([0, -1, 0, -143568404096, 20939829008363520]\) | \(-45100802713464654722769650329/4293192974400000000000\) | \(-31152755666620573286400000000000\) | \([]\) | \(1938816000\) | \(5.0799\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 493680.bt1 has rank \(1\).
Complex multiplication
The elliptic curves in class 493680.bt do not have complex multiplication.Modular form 493680.2.a.bt
sage: E.q_eigenform(10)