Cremona's table of elliptic curves

2006 = 2 · 17 · 59

Field	Data	Notes
Atkin-Lehner	2- 17+ 59+	Signs for the Atkin-Lehner involutions
Class	2006h	Isogeny class
Conductor	2006	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	7612392968095424 = 26 · 1710 · 59	Discriminant
Eigenvalues	2-  2 -2  2  4  2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-49719,-786739]	[a1,a2,a3,a4,a6]
j	13592251860742707697/7612392968095424	j-invariant
L	4.1229008398178	L(r)(E,1)/r!
Ω	0.34357506998481	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	16048t2 64192m2 18054k2 50150k2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2006h2

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

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Quadratic twists for elliptic curve 2006h2

-4	8	-3	5	-7	17	-59
16048t2	64192m2	18054k2	50150k2	98294w2	34102o2	118354d2

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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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