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	3192a	Isogeny class
Conductor	3192	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	140141568 = 210 · 3 · 74 · 19	Discriminant
Eigenvalues	2+ 3+  2 7+  4 -6  6 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1232,17052]	[a1,a2,a3,a4,a6]
j	202119559492/136857	j-invariant
L	1.8217734478846	L(r)(E,1)/r!
Ω	1.8217734478846	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	6384k3 25536bc4 9576w3 79800bt4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3192a3

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	6	-	8	-6	0	-2	6	-4	4	2	12	-10	8	0	10	-12	16	6	-10

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Quadratic twists for elliptic curve 3192a3

-4	8	-3	5	-7	-19
6384k3	25536bc4	9576w3	79800bt4	22344u4	60648bi4

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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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