Cremona's table of elliptic curves

5593 = 7 · 17 · 47

Field	Data	Notes
Atkin-Lehner	7- 17- 47+	Signs for the Atkin-Lehner involutions
Class	5593c	Isogeny class
Conductor	5593	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	174720	Modular degree for the optimal curve
Δ	-5510353099611689 = -1 · 75 · 178 · 47	Discriminant
Eigenvalues	-1 -3 -1 7-  5  2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-4415058,-3569592462]	[a1,a2,a3,a4,a6]
Generators	[3178:118779:1]	Generators of the group modulo torsion
j	-9517718582850347460282609/5510353099611689	j-invariant
L	1.5412709076261	L(r)(E,1)/r!
Ω	0.052075739794863	Real period
R	0.73991791268712	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	89488e1 50337n1 39151f1 95081b1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 5593c1

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	-1	-	5	2	-	4	-4	-2	-2	-7	7	1	+	-9	9	-4	-4	4	-1	12	5	-4	-10

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Quadratic twists for elliptic curve 5593c1

-4	-3	-7	17
89488e1	50337n1	39151f1	95081b1

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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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