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	8050u	Isogeny class
Conductor	8050	Conductor
∏ cp	40	Product of Tamagawa factors cp
deg	9600	Modular degree for the optimal curve
Δ	-274244180000 = -1 · 25 · 54 · 72 · 234	Discriminant
Eigenvalues	2-  1 5- 7- -5  2 -5  5	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-963,27617]	[a1,a2,a3,a4,a6]
Generators	[-32:177:1]	Generators of the group modulo torsion
j	-158034076225/438790688	j-invariant
L	7.1723544843829	L(r)(E,1)/r!
Ω	0.86234104234998	Real period
R	0.20793265460372	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	64400cc1 72450cd1 8050a1 56350cb1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8050u1

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	2	-5	5	-	-2	-4	4	-5	-8	-6	-4	4	10	1	2	-15	-10	3	-15	-2

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Quadratic twists for elliptic curve 8050u1

-4	-3	5	-7
64400cc1	72450cd1	8050a1	56350cb1

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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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