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	6006bc	Isogeny class
Conductor	6006	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	41225184 = 25 · 32 · 7 · 112 · 132	Discriminant
Eigenvalues	2- 3- -2 7+ 11- 13-  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-10749,428049]	[a1,a2,a3,a4,a6]
Generators	[24:417:1]	Generators of the group modulo torsion
j	137350557323428177/41225184	j-invariant
L	6.1088208052027	L(r)(E,1)/r!
Ω	1.6362580171742	Real period
R	0.37334092429704	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	48048bq2 18018g2 42042cj2 66066bd2	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006bc2

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	+	-	-	0	-4	-4	-8	4	0	-10	-4	4	14	14	-14	-8	-10	-10	-6	-4	0	-4

---

Quadratic twists for elliptic curve 6006bc2

-4	-3	-7	-11	13
48048bq2	18018g2	42042cj2	66066bd2	78078bl2

---

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