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	17136d	Isogeny class
Conductor	17136	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	1309309940736 = 210 · 37 · 7 · 174	Discriminant
Eigenvalues	2+ 3-  2 7+ -4  6 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4899,-119950]	[a1,a2,a3,a4,a6]
j	17418812548/1753941	j-invariant
L	2.2974276191588	L(r)(E,1)/r!
Ω	0.5743569047897	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	8568k3 68544dp4 5712b3 119952bm4	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17136d3

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

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Quadratic twists for elliptic curve 17136d3

-4	8	-3	-7
8568k3	68544dp4	5712b3	119952bm4

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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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