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	3192b	Isogeny class
Conductor	3192	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	3028319142912 = 210 · 33 · 78 · 19	Discriminant
Eigenvalues	2+ 3+ -2 7+  0 -2  2 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-11744,486588]	[a1,a2,a3,a4,a6]
j	174947951977348/2957342913	j-invariant
L	0.80190297998182	L(r)(E,1)/r!
Ω	0.80190297998182	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	6384m3 25536z3 9576u3 79800bs3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3192b4

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	-2	2	-	-4	2	0	-10	-10	4	12	-6	-4	14	-4	-16	10	16	8	6	18

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Quadratic twists for elliptic curve 3192b4

-4	8	-3	5	-7	-19
6384m3	25536z3	9576u3	79800bs3	22344s3	60648bj3

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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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