Show commands:
SageMath
E = EllipticCurve("dk1")
E.isogeny_class()
Elliptic curves in class 289800dk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 289800.dk1 | 289800dk1 | \([0, 0, 0, -466097700, 3873143216500]\) | \(-3840316976122235063296/27784071875\) | \(-81018353587500000000\) | \([]\) | \(51840000\) | \(3.4165\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 289800dk1 has rank \(1\).
Complex multiplication
The elliptic curves in class 289800dk do not have complex multiplication.Modular form 289800.2.a.dk
sage: E.q_eigenform(10)