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	17328t	Isogeny class
Conductor	17328	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-8215448895553609728 = -1 · 213 · 310 · 198	Discriminant
Eigenvalues	2- 3+  0 -4 -4  0 -2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-493968,-191860416]	[a1,a2,a3,a4,a6]
Generators	[4963630:596362614:343]	Generators of the group modulo torsion
j	-69173457625/42633378	j-invariant
L	2.9399578747017	L(r)(E,1)/r!
Ω	0.087587721854289	Real period
R	8.3914668987298	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	2166i2 69312di2 51984cn2 912h2	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 17328t2

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	-4	-4	0	-2	-	2	6	6	8	-10	12	-10	-2	4	-10	0	-16	-2	10	16	2	10

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Quadratic twists for elliptic curve 17328t2

-4	8	-3	-19
2166i2	69312di2	51984cn2	912h2

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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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