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	17328bd	Isogeny class
Conductor	17328	Conductor
∏ cp	108	Product of Tamagawa factors cp
deg	590976	Modular degree for the optimal curve
Δ	-2.1907863721476E+19	Discriminant
Eigenvalues	2- 3- -4  3 -2 -7  0 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,505280,177935924]	[a1,a2,a3,a4,a6]
Generators	[842:-34656:1]	Generators of the group modulo torsion
j	205083359/314928	j-invariant
L	4.5464627932393	L(r)(E,1)/r!
Ω	0.14604455147407	Real period
R	0.28824682119452	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	2166g1 69312ck1 51984ch1 17328y1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 17328bd1

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 17328bd1

-4	8	-3	-19
2166g1	69312ck1	51984ch1	17328y1

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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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