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	5290c	Isogeny class
Conductor	5290	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	-26450 = -1 · 2 · 52 · 232	Discriminant
Eigenvalues	2+  1 5-  4  0 -4 -3  1	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-23,-44]	[a1,a2,a3,a4,a6]
Generators	[10:22:1]	Generators of the group modulo torsion
j	-2387929/50	j-invariant
L	3.8245910882933	L(r)(E,1)/r!
Ω	1.0944222742102	Real period
R	1.747310511865	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	42320x1 47610ca1 26450q1 5290a1	Quadratic twists by: -4 -3 5 -23

Hecke Eigenvalues for elliptic curve 5290c1

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	-	4	0	-4	-3	1	-	-6	-4	-2	-6	-11	0	6	3	-8	13	-12	-7	10	9	-6	-14

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Quadratic twists for elliptic curve 5290c1

-4	-3	5	-23
42320x1	47610ca1	26450q1	5290a1

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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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