Cremona's table of elliptic curves

5590 = 2 · 5 · 13 · 43

Field	Data	Notes
Atkin-Lehner	2+ 5- 13+ 43+	Signs for the Atkin-Lehner involutions
Class	5590b	Isogeny class
Conductor	5590	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	6192	Modular degree for the optimal curve
Δ	-18894200 = -1 · 23 · 52 · 133 · 43	Discriminant
Eigenvalues	2+  1 5- -5 -5 13+  2 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-4408,-112994]	[a1,a2,a3,a4,a6]
j	-9469059237951481/18894200	j-invariant
L	0.58593698123518	L(r)(E,1)/r!
Ω	0.29296849061759	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	44720q1 50310bw1 27950n1 72670n1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5590b1

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	-	-5	-5	+	2	-6	3	-1	-2	8	8	+	-2	-8	-7	-6	0	-8	1	4	-12	-3	0

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Quadratic twists for elliptic curve 5590b1

-4	-3	5	13
44720q1	50310bw1	27950n1	72670n1

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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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