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	5593b	Isogeny class
Conductor	5593	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	-665567 = -1 · 72 · 172 · 47	Discriminant
Eigenvalues	-1  0  2 7- -4 -4 17-  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-39,110]	[a1,a2,a3,a4,a6]
Generators	[0:10:1]	Generators of the group modulo torsion
j	-6403769793/665567	j-invariant
L	2.5737775393973	L(r)(E,1)/r!
Ω	2.8000186910314	Real period
R	0.91920012807104	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	89488d1 50337p1 39151d1 95081a1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 5593b1

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

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Quadratic twists for elliptic curve 5593b1

-4	-3	-7	17
89488d1	50337p1	39151d1	95081a1

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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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