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	17328f	Isogeny class
Conductor	17328	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	6912	Modular degree for the optimal curve
Δ	-2258202288 = -1 · 24 · 3 · 196	Discriminant
Eigenvalues	2+ 3+ -2  0 -4  2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,241,1698]	[a1,a2,a3,a4,a6]
j	2048/3	j-invariant
L	0.98947723974896	L(r)(E,1)/r!
Ω	0.98947723974896	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	8664g1 69312dl1 51984v1 48a4	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 17328f1

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	2	-	8	-6	8	-6	6	-4	0	2	4	-2	-4	8	10	-8	4	6	-2

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Quadratic twists for elliptic curve 17328f1

-4	8	-3	-19
8664g1	69312dl1	51984v1	48a4

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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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