Cremona's table of elliptic curves

8050 = 2 · 5² · 7 · 23

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 23-	Signs for the Atkin-Lehner involutions
Class	8050o	Isogeny class
Conductor	8050	Conductor
∏ cp	27	Product of Tamagawa factors cp
Δ	-1090163200 = -1 · 29 · 52 · 7 · 233	Discriminant
Eigenvalues	2-  2 5+ 7+ -6  1  3 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-158,-1829]	[a1,a2,a3,a4,a6]
Generators	[29:123:1]	Generators of the group modulo torsion
j	-17455277065/43606528	j-invariant
L	8.0593705846514	L(r)(E,1)/r!
Ω	0.62713847749316	Real period
R	0.47596379037706	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	64400bu2 72450bc2 8050m2 56350br2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8050o2

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
-	2	+	+	-6	1	3	-4	-	-6	8	-11	0	-8	-3	-9	0	8	-8	-6	-2	-1	9	3	1

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Quadratic twists for elliptic curve 8050o2

-4	-3	5	-7
64400bu2	72450bc2	8050m2	56350br2

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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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