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	17328y	Isogeny class
Conductor	17328	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	31104	Modular degree for the optimal curve
Δ	-465670176768 = -1 · 216 · 39 · 192	Discriminant
Eigenvalues	2- 3+ -4  3 -2  7  0 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,1400,-26384]	[a1,a2,a3,a4,a6]
Generators	[20:96:1]	Generators of the group modulo torsion
j	205083359/314928	j-invariant
L	3.5982661598643	L(r)(E,1)/r!
Ω	0.49478004491324	Real period
R	1.8181140270599	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	2166e1 69312du1 51984cx1 17328bd1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 17328y1

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
-	+	-4	3	-2	7	0	-	4	-4	1	-7	-4	-7	-2	4	-6	-1	3	2	-3	5	12	-18	-10

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Quadratic twists for elliptic curve 17328y1

-4	8	-3	-19
2166e1	69312du1	51984cx1	17328bd1

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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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