Cremona's table of elliptic curves

4539 = 3 · 17 · 89

Field	Data	Notes
Atkin-Lehner	3+ 17- 89-	Signs for the Atkin-Lehner involutions
Class	4539c	Isogeny class
Conductor	4539	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-1141664748816681 = -1 · 312 · 176 · 89	Discriminant
Eigenvalues	1 3+ -2 -4  2  2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-74141,-7969470]	[a1,a2,a3,a4,a6]
Generators	[21844:153893:64]	Generators of the group modulo torsion
j	-45072140451788903257/1141664748816681	j-invariant
L	2.8710928275944	L(r)(E,1)/r!
Ω	0.14444565672096	Real period
R	6.6255432268223	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	72624z2 13617c2 113475k2 77163d2	Quadratic twists by: -4 -3 5 17

Hecke Eigenvalues for elliptic curve 4539c2

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

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Quadratic twists for elliptic curve 4539c2

-4	-3	5	17
72624z2	13617c2	113475k2	77163d2

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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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