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	4592a	Isogeny class
Conductor	4592	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-484058810368 = -1 · 211 · 78 · 41	Discriminant
Eigenvalues	2+  0 -2 7+  0  2  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,949,-31526]	[a1,a2,a3,a4,a6]
j	46152198846/236356841	j-invariant
L	0.93803561050996	L(r)(E,1)/r!
Ω	0.46901780525498	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2296b4 18368v4 41328i3 114800m3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4592a4

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	-2	+	0	2	2	0	-8	-6	8	-2	-	-4	0	10	-12	14	-8	0	10	0	-12	-14	2

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Quadratic twists for elliptic curve 4592a4

-4	8	-3	5	-7
2296b4	18368v4	41328i3	114800m3	32144c3

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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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