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	6006h	Isogeny class
Conductor	6006	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	288927801457206912 = 27 · 33 · 7 · 114 · 138	Discriminant
Eigenvalues	2+ 3+ -2 7- 11- 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-201021,-23205699]	[a1,a2,a3,a4,a6]
Generators	[1109:32902:1]	Generators of the group modulo torsion
j	898362003697422318937/288927801457206912	j-invariant
L	2.2243425251256	L(r)(E,1)/r!
Ω	0.23121785525949	Real period
R	4.8100578621604	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	48048cb3 18018bk4 42042bp3 66066br3	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006h3

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	2	-4	-10	2	8	0	2	-12	2	-4	-12	14	16	8	-6	10

---

Quadratic twists for elliptic curve 6006h3

-4	-3	-7	-11	13
48048cb3	18018bk4	42042bp3	66066br3	78078bu3

---

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