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	3192m	Isogeny class
Conductor	3192	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-704841280512768 = -1 · 28 · 33 · 710 · 192	Discriminant
Eigenvalues	2- 3+ -4 7+  0 -2  4 19-	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-106300,-13365404]	[a1,a2,a3,a4,a6]
Generators	[396:2546:1]	Generators of the group modulo torsion
j	-518904725785387216/2753286252003	j-invariant
L	2.1311543285757	L(r)(E,1)/r!
Ω	0.13215941378274	Real period
R	4.03140848536	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	6384o2 25536be2 9576k2 79800m2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3192m2

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
-	+	-4	+	0	-2	4	-	4	4	0	-10	10	4	-6	0	4	-10	-4	-2	-2	4	-14	-6	-18

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Quadratic twists for elliptic curve 3192m2

-4	8	-3	5	-7	-19
6384o2	25536be2	9576k2	79800m2	22344bg2	60648q2

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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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