Cremona's table of elliptic curves

8800 = 2⁵ · 5² · 11

Field	Data	Notes
Atkin-Lehner	2- 5+ 11-	Signs for the Atkin-Lehner involutions
Class	8800u	Isogeny class
Conductor	8800	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	440000000 = 29 · 57 · 11	Discriminant
Eigenvalues	2-  0 5+  0 11-  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-14675,684250]	[a1,a2,a3,a4,a6]
Generators	[2478:8974:27]	Generators of the group modulo torsion
j	43688592648/55	j-invariant
L	4.2078571798972	L(r)(E,1)/r!
Ω	1.4147546464541	Real period
R	5.9485327585865	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	8800a2 17600a3 79200t4 1760f3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8800u3

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

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Quadratic twists for elliptic curve 8800u3

-4	8	-3	5	-11
8800a2	17600a3	79200t4	1760f3	96800d4

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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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