Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 28322j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28322.l1 | 28322j1 | \([1, -1, 0, -21640663, -139663885411]\) | \(-164384733177/1140850688\) | \(-7778623244332216277270528\) | \([]\) | \(12579840\) | \(3.4594\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 28322j1 has rank \(0\).
Complex multiplication
The elliptic curves in class 28322j do not have complex multiplication.Modular form 28322.2.a.j
sage: E.q_eigenform(10)