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	4592h	Isogeny class
Conductor	4592	Conductor
∏ cp	10	Product of Tamagawa factors cp
Δ	6643657990144 = 213 · 7 · 415	Discriminant
Eigenvalues	2-  1  1 7+ -2  4  3  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-252560,48769172]	[a1,a2,a3,a4,a6]
Generators	[287:82:1]	Generators of the group modulo torsion
j	434969885624052241/1621986814	j-invariant
L	4.4328216143409	L(r)(E,1)/r!
Ω	0.65779394988126	Real period
R	0.67389212307913	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	574j2 18368x2 41328bd2 114800ca2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 4592h2

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	1	+	-2	4	3	0	-4	-5	-7	-2	-	1	2	-1	-10	-13	2	3	4	15	6	-15	-7

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Quadratic twists for elliptic curve 4592h2

-4	8	-3	5	-7
574j2	18368x2	41328bd2	114800ca2	32144s2

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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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