Cremona's table of elliptic curves

3944 = 2³ · 17 · 29

Field	Data	Notes
Atkin-Lehner	2- 17+ 29-	Signs for the Atkin-Lehner involutions
Class	3944b	Isogeny class
Conductor	3944	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	512	Modular degree for the optimal curve
Δ	-504832 = -1 · 210 · 17 · 29	Discriminant
Eigenvalues	2- -2  4 -1 -4  1 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-16,-48]	[a1,a2,a3,a4,a6]
Generators	[8:20:1]	Generators of the group modulo torsion
j	-470596/493	j-invariant
L	3.0873691119966	L(r)(E,1)/r!
Ω	1.1398658591334	Real period
R	1.3542686129506	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	7888a1 31552c1 35496c1 98600e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3944b1

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	4	-1	-4	1	+	-1	0	-	4	-1	-5	-11	-7	3	6	-7	-2	-3	-1	0	-4	2	2

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Quadratic twists for elliptic curve 3944b1

-4	8	-3	5	17	29
7888a1	31552c1	35496c1	98600e1	67048b1	114376c1

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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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