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	6006bd	Isogeny class
Conductor	6006	Conductor
∏ cp	1024	Product of Tamagawa factors cp
deg	98304	Modular degree for the optimal curve
Δ	-425928037217050368 = -1 · 28 · 38 · 7 · 118 · 132	Discriminant
Eigenvalues	2- 3- -2 7+ 11- 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,83616,-29981952]	[a1,a2,a3,a4,a6]
Generators	[246:2220:1]	Generators of the group modulo torsion
j	64653427259057355263/425928037217050368	j-invariant
L	6.0797735379341	L(r)(E,1)/r!
Ω	0.14877829136818	Real period
R	2.5540409331663	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	8	Number of elements in the torsion subgroup
Twists	48048bs1 18018h1 42042ck1 66066be1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006bd1

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

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Quadratic twists for elliptic curve 6006bd1

-4	-3	-7	-11	13
48048bs1	18018h1	42042ck1	66066be1	78078bm1

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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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