Cremona's table of elliptic curves

12006 = 2 · 3² · 23 · 29

Field	Data	Notes
Atkin-Lehner	2- 3- 23- 29-	Signs for the Atkin-Lehner involutions
Class	12006s	Isogeny class
Conductor	12006	Conductor
∏ cp	96	Product of Tamagawa factors cp
deg	30720	Modular degree for the optimal curve
Δ	-50572010520576 = -1 · 216 · 37 · 233 · 29	Discriminant
Eigenvalues	2- 3-  1  0 -5  3 -4  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-6287,-390697]	[a1,a2,a3,a4,a6]
Generators	[123:766:1]	Generators of the group modulo torsion
j	-37693095294889/69371756544	j-invariant
L	7.260819099157	L(r)(E,1)/r!
Ω	0.25267116625385	Real period
R	0.29933582610252	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	96048ba1 4002d1	Quadratic twists by: -4 -3

Hecke Eigenvalues for elliptic curve 12006s1

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
-	-	1	0	-5	3	-4	4	-	-	5	-3	-9	-6	-10	-6	7	1	-13	5	-4	-2	6	10	18

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Quadratic twists for elliptic curve 12006s1

-4	-3
96048ba1	4002d1

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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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