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	8	Product of Tamagawa factors cp
deg	6144	Modular degree for the optimal curve
Δ	-1798868736 = -1 · 28 · 310 · 7 · 17	Discriminant
Eigenvalues	2+ 3- -2 7+ -4  2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,249,-1370]	[a1,a2,a3,a4,a6]
Generators	[9:40:1]	Generators of the group modulo torsion
j	9148592/9639	j-invariant
L	3.7854764271304	L(r)(E,1)/r!
Ω	0.80565273295187	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	8568g1 68544dz1 5712j1 119952x1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17136g1

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 17136g1

-4	8	-3	-7
8568g1	68544dz1	5712j1	119952x1

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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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