Cremona's table of elliptic curves

3192 = 2³ · 3 · 7 · 19

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 19+	Signs for the Atkin-Lehner involutions
Class	3192j	Isogeny class
Conductor	3192	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1280	Modular degree for the optimal curve
Δ	715008 = 28 · 3 · 72 · 19	Discriminant
Eigenvalues	2- 3+  2 7+ -4 -6  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-932,11268]	[a1,a2,a3,a4,a6]
j	350104249168/2793	j-invariant
L	1.2820270828047	L(r)(E,1)/r!
Ω	2.5640541656094	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	6384p1 25536bj1 9576g1 79800k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3192j1

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

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Quadratic twists for elliptic curve 3192j1

-4	8	-3	5	-7	-19
6384p1	25536bj1	9576g1	79800k1	22344bj1	60648o1

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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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