Cremona's table of elliptic curves

17328 = 2⁴ · 3 · 19²

Field	Data	Notes
Atkin-Lehner	2- 3- 19+	Signs for the Atkin-Lehner involutions
Class	17328z	Isogeny class
Conductor	17328	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	34560	Modular degree for the optimal curve
Δ	-33206307913728 = -1 · 220 · 35 · 194	Discriminant
Eigenvalues	2- 3-  0 -1  2 -3  4 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-17448,-935244]	[a1,a2,a3,a4,a6]
Generators	[174:1152:1]	Generators of the group modulo torsion
j	-1100553625/62208	j-invariant
L	5.9457564025102	L(r)(E,1)/r!
Ω	0.20701805081434	Real period
R	1.4360478178404	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	2166a1 69312cb1 51984bw1 17328r1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 17328z1

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
-	-	0	-1	2	-3	4	+	-4	0	3	-5	4	9	-10	-4	14	11	-3	-14	-11	-1	-8	-14	2

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Quadratic twists for elliptic curve 17328z1

-4	8	-3	-19
2166a1	69312cb1	51984bw1	17328r1

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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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