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	6006i	Isogeny class
Conductor	6006	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	19163006232001632 = 25 · 38 · 74 · 113 · 134	Discriminant
Eigenvalues	2+ 3+ -2 7- 11- 13+ -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-241131,44985501]	[a1,a2,a3,a4,a6]
Generators	[11:6501:1]	Generators of the group modulo torsion
j	1550549616695674282297/19163006232001632	j-invariant
L	2.1682225814953	L(r)(E,1)/r!
Ω	0.38747765079955	Real period
R	0.46631132079945	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	48048cc4 18018bj3 42042bo4 66066bq4	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 6006i3

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	0	0	-6	8	10	2	0	0	-2	-4	2	-4	-12	-6	-16	0	10	18

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Quadratic twists for elliptic curve 6006i3

-4	-3	-7	-11	13
48048cc4	18018bj3	42042bo4	66066bq4	78078bv4

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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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