Cremona's table of elliptic curves

2006 = 2 · 17 · 59

Field	Data	Notes
Atkin-Lehner	2- 17- 59+	Signs for the Atkin-Lehner involutions
Class	2006i	Isogeny class
Conductor	2006	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	236708 = 22 · 17 · 592	Discriminant
Eigenvalues	2-  0  0  2 -6 -2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-40,103]	[a1,a2,a3,a4,a6]
Generators	[1:7:1]	Generators of the group modulo torsion
j	6913292625/236708	j-invariant
L	4.1929585228454	L(r)(E,1)/r!
Ω	3.11135727657	Real period
R	1.3476300373539	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	16048x1 64192w1 18054b1 50150a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2006i1

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
-	0	0	2	-6	-2	-	-4	-8	4	-4	-2	-2	8	8	2	+	6	-12	6	8	-10	4	6	-8

---

Quadratic twists for elliptic curve 2006i1

-4	8	-3	5	-7	17	-59
16048x1	64192w1	18054b1	50150a1	98294o1	34102k1	118354g1

---

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