Cremona's table of elliptic curves

33984 = 2⁶ · 3² · 59

Field	Data	Notes
Atkin-Lehner	2- 3- 59+	Signs for the Atkin-Lehner involutions
Class	33984bl	Isogeny class
Conductor	33984	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-125045842411782144 = -1 · 219 · 39 · 594	Discriminant
Eigenvalues	2- 3-  2  0 -4  6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,124116,2490320]	[a1,a2,a3,a4,a6]
Generators	[3785333305:101913253805:10793861]	Generators of the group modulo torsion
j	1106469823607/654337494	j-invariant
L	6.9121778565001	L(r)(E,1)/r!
Ω	0.20108983806396	Real period
R	17.186790548563	Regulator
r	1	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	33984w3 8496v4 11328o4	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 33984bl3

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	6	-2	4	8	2	-8	-2	-2	0	8	-6	+	-10	-8	-12	-14	16	-4	-6	2

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Quadratic twists for elliptic curve 33984bl3

-4	8	-3
33984w3	8496v4	11328o4

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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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