Cremona's table of elliptic curves

17136 = 2⁴ · 3² · 7 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 17-	Signs for the Atkin-Lehner involutions
Class	17136g	Isogeny class
Conductor	17136	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	182818363392 = 211 · 37 · 74 · 17	Discriminant
Eigenvalues	2+ 3- -2 7+ -4  2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-19731,-1066574]	[a1,a2,a3,a4,a6]
Generators	[-81:14:1]	Generators of the group modulo torsion
j	569001644066/122451	j-invariant
L	3.7854764271304	L(r)(E,1)/r!
Ω	0.40282636647593	Real period
R	2.3493226500086	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	8568g4 68544dz4 5712j4 119952x4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17136g3

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

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Quadratic twists for elliptic curve 17136g3

-4	8	-3	-7
8568g4	68544dz4	5712j4	119952x4

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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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