Cremona's table of elliptic curves

4592 = 2⁴ · 7 · 41

Field	Data	Notes
Atkin-Lehner	2- 7+ 41-	Signs for the Atkin-Lehner involutions
Class	4592i	Isogeny class
Conductor	4592	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1887503908864 = 227 · 73 · 41	Discriminant
Eigenvalues	2- -1 -3 7+  0  2 -3  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-37352,2790256]	[a1,a2,a3,a4,a6]
Generators	[164:1024:1]	Generators of the group modulo torsion
j	1407074115849193/460816384	j-invariant
L	2.303307831147	L(r)(E,1)/r!
Ω	0.81611853623967	Real period
R	0.70556779709956	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	574f2 18368w2 41328bf2 114800bz2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4592i2

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

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Quadratic twists for elliptic curve 4592i2

-4	8	-3	5	-7
574f2	18368w2	41328bf2	114800bz2	32144o2

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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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