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	2006c	Isogeny class
Conductor	2006	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	1664	Modular degree for the optimal curve
Δ	-22785865136 = -1 · 24 · 176 · 59	Discriminant
Eigenvalues	2+  1 -3 -1  0 -4 17- -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,30,-7260]	[a1,a2,a3,a4,a6]
j	3131359847/22785865136	j-invariant
L	0.74197967913496	L(r)(E,1)/r!
Ω	0.55648475935122	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	16048bc1 64192bd1 18054q1 50150z1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2006c1

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
+	1	-3	-1	0	-4	-	-1	6	-9	8	8	-3	8	6	3	+	2	8	-12	2	17	12	0	-16

---

Quadratic twists for elliptic curve 2006c1

-4	8	-3	5	-7	17	-59
16048bc1	64192bd1	18054q1	50150z1	98294e1	34102f1	118354s1

---

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