Cremona's table of elliptic curves

8084 = 2² · 43 · 47

Field	Data	Notes
Atkin-Lehner	2- 43- 47+	Signs for the Atkin-Lehner involutions
Class	8084b	Isogeny class
Conductor	8084	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	2376	Modular degree for the optimal curve
Δ	32336 = 24 · 43 · 47	Discriminant
Eigenvalues	2- -2  3  2  0 -4 -3 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1349,18628]	[a1,a2,a3,a4,a6]
Generators	[91:811:1]	Generators of the group modulo torsion
j	16980930199552/2021	j-invariant
L	3.7376262774128	L(r)(E,1)/r!
Ω	2.8649009575032	Real period
R	3.9138800951816	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	32336j1 129344g1 72756j1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 8084b1

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	3	2	0	-4	-3	-1	0	3	-4	8	0	-	+	-3	-9	-4	-4	12	-7	5	-3	-6	11

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Quadratic twists for elliptic curve 8084b1

-4	8	-3
32336j1	129344g1	72756j1

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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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