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	17136j	Isogeny class
Conductor	17136	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	6346408900608 = 211 · 312 · 73 · 17	Discriminant
Eigenvalues	2+ 3-  2 7-  0  2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1632306819,25383459170018]	[a1,a2,a3,a4,a6]
Generators	[28951:1546650:1]	Generators of the group modulo torsion
j	322159999717985454060440834/4250799	j-invariant
L	6.1111900734346	L(r)(E,1)/r!
Ω	0.17303843986917	Real period
R	5.8861584725095	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	8568c3 68544em4 5712g3 119952bk4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17136j4

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

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Quadratic twists for elliptic curve 17136j4

-4	8	-3	-7
8568c3	68544em4	5712g3	119952bk4

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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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