Cremona's table of elliptic curves

6006 = 2 · 3 · 7 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 11- 13+	Signs for the Atkin-Lehner involutions
Class	6006bf	Isogeny class
Conductor	6006	Conductor
∏ cp	240	Product of Tamagawa factors cp
Δ	7695534223160784 = 24 · 35 · 712 · 11 · 13	Discriminant
Eigenvalues	2- 3- -2 7- 11- 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2967699,1967534289]	[a1,a2,a3,a4,a6]
Generators	[1008:231:1]	Generators of the group modulo torsion
j	2890568544635035786835377/7695534223160784	j-invariant
L	6.3451233385098	L(r)(E,1)/r!
Ω	0.36145282692232	Real period
R	0.29257498562753	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	48048bc4 18018k3 42042co4 66066x4	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006bf3

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	-	-	+	-2	-4	-4	-6	0	-10	-2	-4	0	-2	4	10	-8	16	-10	-8	8	-6	6

---

Quadratic twists for elliptic curve 6006bf3

-4	-3	-7	-11	13
48048bc4	18018k3	42042co4	66066x4	78078z4

---

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