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	8184c	Isogeny class
Conductor	8184	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-4861296 = -1 · 24 · 34 · 112 · 31	Discriminant
Eigenvalues	2+ 3+  1  3 11- -2  4 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3220,71413]	[a1,a2,a3,a4,a6]
Generators	[34:9:1]	Generators of the group modulo torsion
j	-230837419975936/303831	j-invariant
L	4.3106821101947	L(r)(E,1)/r!
Ω	2.062557614814	Real period
R	0.26124616345465	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	16368i1 65472s1 24552n1 90024u1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8184c1

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
+	+	1	3	-	-2	4	-5	-6	6	-	0	-7	-2	0	-10	3	-6	-8	-9	-6	-14	0	-10	17

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Quadratic twists for elliptic curve 8184c1

-4	8	-3	-11
16368i1	65472s1	24552n1	90024u1

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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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