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	6006r	Isogeny class
Conductor	6006	Conductor
∏ cp	36	Product of Tamagawa factors cp
Δ	4807849294248 = 23 · 3 · 73 · 112 · 136	Discriminant
Eigenvalues	2+ 3-  0 7- 11- 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-43401,-3482108]	[a1,a2,a3,a4,a6]
Generators	[262:1643:1]	Generators of the group modulo torsion
j	9040834853442015625/4807849294248	j-invariant
L	3.6591451359823	L(r)(E,1)/r!
Ω	0.33078033392339	Real period
R	1.2291289417163	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	48048be4 18018bm4 42042p4 66066ci4	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006r4

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

---

Quadratic twists for elliptic curve 6006r4

-4	-3	-7	-11	13
48048be4	18018bm4	42042p4	66066ci4	78078ct4

---

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