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	16	Product of Tamagawa factors cp
Δ	4132946944 = 210 · 74 · 412	Discriminant
Eigenvalues	2+  0 -2 7+  0  2  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-691,-6270]	[a1,a2,a3,a4,a6]
j	35633452068/4036081	j-invariant
L	0.93803561050996	L(r)(E,1)/r!
Ω	0.93803561050996	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2296b2 18368v2 41328i2 114800m2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4592a2

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 4592a2

-4	8	-3	5	-7
2296b2	18368v2	41328i2	114800m2	32144c2

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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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