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	6006h	Isogeny class
Conductor	6006	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	21504	Modular degree for the optimal curve
Δ	-94315065901056 = -1 · 228 · 33 · 7 · 11 · 132	Discriminant
Eigenvalues	2+ 3+ -2 7- 11- 13+  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,1859,467005]	[a1,a2,a3,a4,a6]
Generators	[-21:658:1]	Generators of the group modulo torsion
j	709899390552743/94315065901056	j-invariant
L	2.2243425251256	L(r)(E,1)/r!
Ω	0.46243571051899	Real period
R	4.8100578621604	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	48048cb1 18018bk1 42042bp1 66066br1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006h1

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	-	-	+	2	4	-4	2	-4	-10	2	8	0	2	-12	2	-4	-12	14	16	8	-6	10

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Quadratic twists for elliptic curve 6006h1

-4	-3	-7	-11	13
48048cb1	18018bk1	42042bp1	66066br1	78078bu1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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