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	17136z	Isogeny class
Conductor	17136	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	24440452227072 = 213 · 36 · 72 · 174	Discriminant
Eigenvalues	2- 3- -2 7+  0 -2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-76131,-8081694]	[a1,a2,a3,a4,a6]
Generators	[-161:46:1]	Generators of the group modulo torsion
j	16342588257633/8185058	j-invariant
L	3.7222900143474	L(r)(E,1)/r!
Ω	0.28742346852857	Real period
R	3.2376357725791	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	2142h3 68544dl4 1904c3 119952gl4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17136z3

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

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Quadratic twists for elliptic curve 17136z3

-4	8	-3	-7
2142h3	68544dl4	1904c3	119952gl4

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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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