Cremona's table of elliptic curves

2166 = 2 · 3 · 19²

Field	Data	Notes
Atkin-Lehner	2+ 3- 19-	Signs for the Atkin-Lehner involutions
Class	2166d	Isogeny class
Conductor	2166	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	21600	Modular degree for the optimal curve
Δ	25306896220028928 = 220 · 33 · 197	Discriminant
Eigenvalues	2+ 3-  2  0 -4 -2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-127080,15656374]	[a1,a2,a3,a4,a6]
Generators	[68:2673:1]	Generators of the group modulo torsion
j	4824238966273/537919488	j-invariant
L	2.9073689744586	L(r)(E,1)/r!
Ω	0.36530210425462	Real period
R	1.3264678470216	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17328v1 69312t1 6498w1 54150bv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2166d1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	-	2	0	-4	-2	-6	-	-4	2	-4	-10	-10	4	-4	10	-12	14	12	-8	-6	4	12	6	-10

---

Quadratic twists for elliptic curve 2166d1

-4	8	-3	5	-7	-19
17328v1	69312t1	6498w1	54150bv1	106134q1	114c1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations