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	17136o	Isogeny class
Conductor	17136	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	-1289723904 = -1 · 213 · 33 · 73 · 17	Discriminant
Eigenvalues	2- 3+  3 7+ -3  5 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2691,-53758]	[a1,a2,a3,a4,a6]
j	-19486825371/11662	j-invariant
L	2.6513406664573	L(r)(E,1)/r!
Ω	0.33141758330716	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2142b1 68544cv1 17136r2 119952di1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17136o1

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 17136o1

-4	8	-3	-7
2142b1	68544cv1	17136r2	119952di1

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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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