Cremona's table of elliptic curves

8184 = 2³ · 3 · 11 · 31

Field	Data	Notes
Atkin-Lehner	2+ 3+ 11- 31-	Signs for the Atkin-Lehner involutions
Class	8184d	Isogeny class
Conductor	8184	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	311122944 = 210 · 34 · 112 · 31	Discriminant
Eigenvalues	2+ 3+ -2  0 11- -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-80024,-8686596]	[a1,a2,a3,a4,a6]
Generators	[2746:16335:8]	Generators of the group modulo torsion
j	55346472949076068/303831	j-invariant
L	3.017785238978	L(r)(E,1)/r!
Ω	0.28385335950349	Real period
R	5.3157469128719	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	16368j4 65472t4 24552o4 90024v4	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8184d3

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	0	-6	-	6	2	4	12	2	0	6	4	-12	-6	-8	-12	14	2

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Quadratic twists for elliptic curve 8184d3

-4	8	-3	-11
16368j4	65472t4	24552o4	90024v4

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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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