Show commands:
SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 209484.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 209484.bd1 | 209484w1 | \([0, 0, 0, -144069447, -1424395727138]\) | \(-22628157757264/46877879169\) | \(-685106577456197751776123136\) | \([]\) | \(64862208\) | \(3.8384\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 209484.bd1 has rank \(0\).
Complex multiplication
The elliptic curves in class 209484.bd do not have complex multiplication.Modular form 209484.2.a.bd
sage: E.q_eigenform(10)