Cremona's table of elliptic curves

3168 = 2⁵ · 3² · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 11+	Signs for the Atkin-Lehner involutions
Class	3168u	Isogeny class
Conductor	3168	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-49182515712 = -1 · 29 · 38 · 114	Discriminant
Eigenvalues	2- 3-  2  0 11+ -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,501,9758]	[a1,a2,a3,a4,a6]
Generators	[-11:54:1]	Generators of the group modulo torsion
j	37259704/131769	j-invariant
L	3.7107745074984	L(r)(E,1)/r!
Ω	0.80097925270815	Real period
R	1.1581993213158	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	3168m4 6336bc4 1056c4 79200w2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3168u4

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	+	-6	-2	4	-4	-2	4	-2	-10	4	-4	-6	-12	-6	4	-4	10	16	4	-10	2

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Quadratic twists for elliptic curve 3168u4

-4	8	-3	5	-11
3168m4	6336bc4	1056c4	79200w2	34848t2

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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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