Cremona's table of elliptic curves

32016 = 2⁴ · 3 · 23 · 29

Field	Data	Notes
Atkin-Lehner	2- 3- 23+ 29+	Signs for the Atkin-Lehner involutions
Class	32016bb	Isogeny class
Conductor	32016	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	82944	Modular degree for the optimal curve
Δ	-186924492914688 = -1 · 230 · 32 · 23 · 292	Discriminant
Eigenvalues	2- 3- -2 -2  2 -2  4  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1744,657812]	[a1,a2,a3,a4,a6]
Generators	[148:1914:1]	Generators of the group modulo torsion
j	-143301984337/45635862528	j-invariant
L	5.5089837146747	L(r)(E,1)/r!
Ω	0.46172190494293	Real period
R	2.9828472808516	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	4002j1 128064cg1 96048bq1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 32016bb1

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	-2	2	-2	4	4	+	+	-4	-4	-2	8	0	2	0	8	-8	0	-10	14	-6	-12	18

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Quadratic twists for elliptic curve 32016bb1

-4	8	-3
4002j1	128064cg1	96048bq1

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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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