Cremona's table of elliptic curves

5290 = 2 · 5 · 23²

Field	Data	Notes
Atkin-Lehner	2+ 5+ 23-	Signs for the Atkin-Lehner involutions
Class	5290b	Isogeny class
Conductor	5290	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8832	Modular degree for the optimal curve
Δ	-2773483520000 = -1 · 223 · 54 · 232	Discriminant
Eigenvalues	2+ -1 5+  2  4  4  3  1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-758,80212]	[a1,a2,a3,a4,a6]
j	-91236912601/5242880000	j-invariant
L	1.3347271986991	L(r)(E,1)/r!
Ω	0.66736359934956	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	42320m1 47610cj1 26450n1 5290d1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 5290b1

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	4	3	1	-	8	2	-2	6	3	2	-4	7	-12	-5	-14	11	8	7	18	14

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Quadratic twists for elliptic curve 5290b1

-4	-3	5	-23
42320m1	47610cj1	26450n1	5290d1

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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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