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	72	Product of Tamagawa factors cp
Δ	-1637696668608 = -1 · 26 · 32 · 76 · 11 · 133	Discriminant
Eigenvalues	2+ 3-  0 7- 11- 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-2241,-74060]	[a1,a2,a3,a4,a6]
Generators	[115:1034:1]	Generators of the group modulo torsion
j	-1243857621903625/1637696668608	j-invariant
L	3.6591451359823	L(r)(E,1)/r!
Ω	0.33078033392339	Real period
R	0.61456447085813	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	48048be3 18018bm3 42042p3 66066ci3	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006r3

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 6006r3

-4	-3	-7	-11	13
48048be3	18018bm3	42042p3	66066ci3	78078ct3

---

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