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	6006f	Isogeny class
Conductor	6006	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	-95718534912 = -1 · 28 · 32 · 74 · 113 · 13	Discriminant
Eigenvalues	2+ 3+  4 7- 11+ 13+  4  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-423,-15435]	[a1,a2,a3,a4,a6]
j	-8401330071289/95718534912	j-invariant
L	1.8180603345679	L(r)(E,1)/r!
Ω	0.45451508364196	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	48048cl1 18018bq1 42042bj1 66066bs1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006f1

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
+	+	4	-	+	+	4	0	0	0	-10	10	2	6	-12	-2	-4	-10	14	12	-6	14	12	16	18

---

Quadratic twists for elliptic curve 6006f1

-4	-3	-7	-11	13
48048cl1	18018bq1	42042bj1	66066bs1	78078cg1

---

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