Cremona's table of elliptic curves

40050 = 2 · 3² · 5² · 89

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 89-	Signs for the Atkin-Lehner involutions
Class	40050bo	Isogeny class
Conductor	40050	Conductor
∏ cp	50	Product of Tamagawa factors cp
deg	768000	Modular degree for the optimal curve
Δ	-732740280897780000 = -1 · 25 · 38 · 54 · 895	Discriminant
Eigenvalues	2- 3- 5- -3  3  6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-779630,268336797]	[a1,a2,a3,a4,a6]
Generators	[2813:141171:1]	Generators of the group modulo torsion
j	-115022094387354025/1608209121312	j-invariant
L	8.9075451158636	L(r)(E,1)/r!
Ω	0.28585223631736	Real period
R	0.62322724709952	Regulator
r	1	Rank of the group of rational points
S	0.99999999999977	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	13350d1 40050o2	Quadratic twists by: -3 5

Hecke Eigenvalues for elliptic curve 40050bo1

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
-	-	-	-3	3	6	-2	0	-1	-5	-8	7	8	-4	-2	-6	0	-3	7	-12	-9	10	-6	-	7

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Quadratic twists for elliptic curve 40050bo1

-3	5
13350d1	40050o2

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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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