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	24	Product of Tamagawa factors cp
deg	7200	Modular degree for the optimal curve
Δ	20244571000832 = 212 · 175 · 592	Discriminant
Eigenvalues	2-  2 -2  2  4  2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-30839,2060365]	[a1,a2,a3,a4,a6]
j	3243586268529106417/20244571000832	j-invariant
L	4.1229008398178	L(r)(E,1)/r!
Ω	0.68715013996963	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	16048t1 64192m1 18054k1 50150k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 2006h1

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 2006h1

-4	8	-3	5	-7	17	-59
16048t1	64192m1	18054k1	50150k1	98294w1	34102o1	118354d1

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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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