Cremona's table of elliptic curves

8004 = 2² · 3 · 23 · 29

Field	Data	Notes
Atkin-Lehner	2- 3+ 23+ 29-	Signs for the Atkin-Lehner involutions
Class	8004b	Isogeny class
Conductor	8004	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	3600	Modular degree for the optimal curve
Δ	-619285488 = -1 · 24 · 3 · 232 · 293	Discriminant
Eigenvalues	2- 3+ -2 -5 -3  1 -3  6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,166,-927]	[a1,a2,a3,a4,a6]
Generators	[76:667:1]	Generators of the group modulo torsion
j	31427449088/38705343	j-invariant
L	2.171562925692	L(r)(E,1)/r!
Ω	0.8708448843369	Real period
R	0.13853487220348	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	32016bh1 128064z1 24012f1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 8004b1

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

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Quadratic twists for elliptic curve 8004b1

-4	8	-3
32016bh1	128064z1	24012f1

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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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