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	8050p	Isogeny class
Conductor	8050	Conductor
∏ cp	112	Product of Tamagawa factors cp
Δ	27424418000000 = 27 · 56 · 72 · 234	Discriminant
Eigenvalues	2- -2 5+ 7+  4  0 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-15138,669892]	[a1,a2,a3,a4,a6]
Generators	[-88:1194:1]	Generators of the group modulo torsion
j	24553362849625/1755162752	j-invariant
L	4.3659548730883	L(r)(E,1)/r!
Ω	0.65303083392846	Real period
R	0.23877426861323	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	64400bs2 72450ba2 322b2 56350bp2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8050p2

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

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Quadratic twists for elliptic curve 8050p2

-4	-3	5	-7
64400bs2	72450ba2	322b2	56350bp2

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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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