Show commands:
SageMath
E = EllipticCurve("dk1")
E.isogeny_class()
Elliptic curves in class 88200.dk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88200.dk1 | 88200id1 | \([0, 0, 0, -312375, -159280625]\) | \(-6288640/16807\) | \(-9009194972793750000\) | \([]\) | \(1382400\) | \(2.3245\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 88200.dk1 has rank \(1\).
Complex multiplication
The elliptic curves in class 88200.dk do not have complex multiplication.Modular form 88200.2.a.dk
sage: E.q_eigenform(10)