Cremona's table of elliptic curves

6004 = 2² · 19 · 79

Field	Data	Notes
Atkin-Lehner	2- 19+ 79+	Signs for the Atkin-Lehner involutions
Class	6004a	Isogeny class
Conductor	6004	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	1752	Modular degree for the optimal curve
Δ	-384256 = -1 · 28 · 19 · 79	Discriminant
Eigenvalues	2-  0  1 -4  2 -4  4 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1967,-33578]	[a1,a2,a3,a4,a6]
j	-3287735163216/1501	j-invariant
L	1.0753249235343	L(r)(E,1)/r!
Ω	0.35844164117812	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	24016i1 96064e1 54036c1 114076g1	Quadratic twists by: -4 8 -3 -19

Hecke Eigenvalues for elliptic curve 6004a1

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
-	0	1	-4	2	-4	4	+	-6	-1	5	3	7	-3	3	-9	-6	8	-7	6	-13	+	8	12	16

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Quadratic twists for elliptic curve 6004a1

-4	8	-3	-19
24016i1	96064e1	54036c1	114076g1

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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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