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	3192f	Isogeny class
Conductor	3192	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	23288832 = 210 · 32 · 7 · 192	Discriminant
Eigenvalues	2+ 3-  0 7+  6  4  0 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-168,-864]	[a1,a2,a3,a4,a6]
j	515150500/22743	j-invariant
L	2.6580980142281	L(r)(E,1)/r!
Ω	1.329049007114	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6384e2 25536h2 9576t2 79800bf2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3192f2

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

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Quadratic twists for elliptic curve 3192f2

-4	8	-3	5	-7	-19
6384e2	25536h2	9576t2	79800bf2	22344g2	60648u2

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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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