Cremona's table of elliptic curves

4598 = 2 · 11² · 19

Field	Data	Notes
Atkin-Lehner	2- 11- 19+	Signs for the Atkin-Lehner involutions
Class	4598n	Isogeny class
Conductor	4598	Conductor
∏ cp	54	Product of Tamagawa factors cp
Δ	-4517722956234752 = -1 · 227 · 116 · 19	Discriminant
Eigenvalues	2-  1  0  1 11- -5 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-10348,3258256]	[a1,a2,a3,a4,a6]
Generators	[120:1876:1]	Generators of the group modulo torsion
j	-69173457625/2550136832	j-invariant
L	6.1805473247057	L(r)(E,1)/r!
Ω	0.36260591232978	Real period
R	0.31564455017228	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	36784bh3 41382m3 114950m3 38a2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4598n3

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	0	1	-	-5	-3	+	3	-9	-4	2	0	-8	0	-3	9	10	5	-6	7	10	6	-12	-10

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Quadratic twists for elliptic curve 4598n3

-4	-3	5	-11	-19
36784bh3	41382m3	114950m3	38a2	87362q3

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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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