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	6006k	Isogeny class
Conductor	6006	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	39902230368 = 25 · 34 · 72 · 11 · 134	Discriminant
Eigenvalues	2+ 3-  0 7+ 11+ 13-  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-1656,-24218]	[a1,a2,a3,a4,a6]
Generators	[-28:33:1]	Generators of the group modulo torsion
j	501796540869625/39902230368	j-invariant
L	3.4458112598347	L(r)(E,1)/r!
Ω	0.7522305060766	Real period
R	0.57259896268482	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	48048bw2 18018bh2 42042g2 66066cs2	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006k2

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

---

Quadratic twists for elliptic curve 6006k2

-4	-3	-7	-11	13
48048bw2	18018bh2	42042g2	66066cs2	78078df2

---

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