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	17328v	Isogeny class
Conductor	17328	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	3163362027503616 = 217 · 33 · 197	Discriminant
Eigenvalues	2- 3+  2  0  4 -2 -6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-505700472,-4376948403600]	[a1,a2,a3,a4,a6]
Generators	[-601756767711925009573221845440887341540196818023116614:-14404104601164424404862018805632924910029456570350:46349625241760694261834368249359295129349604873633]	Generators of the group modulo torsion
j	74220219816682217473/16416	j-invariant
L	4.9977989859694	L(r)(E,1)/r!
Ω	0.031836565834652	Real period
R	78.491490130032	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	2166d3 69312do4 51984ct4 912k3	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 17328v3

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

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Quadratic twists for elliptic curve 17328v3

-4	8	-3	-19
2166d3	69312do4	51984ct4	912k3

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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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