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	17328m	Isogeny class
Conductor	17328	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	339023439791364096 = 211 · 33 · 1910	Discriminant
Eigenvalues	2+ 3-  2  0  0 -2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-459312,116340660]	[a1,a2,a3,a4,a6]
Generators	[918:21660:1]	Generators of the group modulo torsion
j	111223479026/3518667	j-invariant
L	6.9837652352722	L(r)(E,1)/r!
Ω	0.30229883876254	Real period
R	1.925182507002	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	8664i3 69312cq4 51984x4 912b3	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 17328m3

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	0	0	-2	2	-	0	-2	-4	-2	-6	4	0	-10	-4	-2	-12	0	-6	-4	8	-6	14

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Quadratic twists for elliptic curve 17328m3

-4	8	-3	-19
8664i3	69312cq4	51984x4	912b3

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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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