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	6006bd	Isogeny class
Conductor	6006	Conductor
∏ cp	512	Product of Tamagawa factors cp
Δ	6219484329456802404 = 22 · 38 · 74 · 112 · 138	Discriminant
Eigenvalues	2- 3- -2 7+ 11- 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-16965284,-26897277396]	[a1,a2,a3,a4,a6]
Generators	[49372:10906234:1]	Generators of the group modulo torsion
j	540016607532350974290947137/6219484329456802404	j-invariant
L	6.0797735379341	L(r)(E,1)/r!
Ω	0.074389145684092	Real period
R	2.5540409331663	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	48048bs4 18018h4 42042ck4 66066be4	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006bd3

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

---

Quadratic twists for elliptic curve 6006bd3

-4	-3	-7	-11	13
48048bs4	18018h4	42042ck4	66066be4	78078bm4

---

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