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	5593a	Isogeny class
Conductor	5593	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	62853604583399 = 73 · 17 · 476	Discriminant
Eigenvalues	-1  0 -2 7+  0  4 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-28936,1862956]	[a1,a2,a3,a4,a6]
Generators	[-19:1560:1]	Generators of the group modulo torsion
j	2679323347758364497/62853604583399	j-invariant
L	1.8208843678632	L(r)(E,1)/r!
Ω	0.62090815057031	Real period
R	1.9550764646813	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	89488l2 50337e2 39151b2 95081c2	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 5593a2

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	0	-2	+	0	4	-	-4	-8	0	10	10	6	-2	-	-6	12	2	-2	-16	-6	0	-4	-2	14

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Quadratic twists for elliptic curve 5593a2

-4	-3	-7	17
89488l2	50337e2	39151b2	95081c2

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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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