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	17136r	Isogeny class
Conductor	17136	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-940208726016 = -1 · 213 · 39 · 73 · 17	Discriminant
Eigenvalues	2- 3+ -3 7+  3  5 17- -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-24219,1451466]	[a1,a2,a3,a4,a6]
Generators	[87:54:1]	Generators of the group modulo torsion
j	-19486825371/11662	j-invariant
L	4.1008392161664	L(r)(E,1)/r!
Ω	0.87275389596528	Real period
R	1.1746837324716	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2142n2 68544da2 17136o1 119952ct2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17136r2

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
-	+	-3	+	3	5	-	-2	0	0	-2	-1	0	-5	-6	3	-12	8	-11	-12	-7	7	-3	9	17

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Quadratic twists for elliptic curve 17136r2

-4	8	-3	-7
2142n2	68544da2	17136o1	119952ct2

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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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