Show commands:
SageMath
E = EllipticCurve("dk1")
E.isogeny_class()
Elliptic curves in class 45570dk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 45570.dj1 | 45570dk1 | \([1, 0, 0, -1129500, -464534568]\) | \(-1354547383894636849/8173828125000\) | \(-961642705078125000\) | \([]\) | \(1544400\) | \(2.2902\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 45570dk1 has rank \(0\).
Complex multiplication
The elliptic curves in class 45570dk do not have complex multiplication.Modular form 45570.2.a.dk
sage: E.q_eigenform(10)