Show commands:
SageMath
E = EllipticCurve("fk1")
E.isogeny_class()
Elliptic curves in class 73920fk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73920.cd1 | 73920fk1 | \([0, -1, 0, -22965, -1332243]\) | \(-81756451446784/24958395\) | \(-408918343680\) | \([]\) | \(138240\) | \(1.2052\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 73920fk1 has rank \(1\).
Complex multiplication
The elliptic curves in class 73920fk do not have complex multiplication.Modular form 73920.2.a.fk
sage: E.q_eigenform(10)