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	16	Product of Tamagawa factors cp
Δ	-585640000000 = -1 · 29 · 57 · 114	Discriminant
Eigenvalues	2-  0 5+  0 11-  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,325,36750]	[a1,a2,a3,a4,a6]
Generators	[-19:154:1]	Generators of the group modulo torsion
j	474552/73205	j-invariant
L	4.2078571798972	L(r)(E,1)/r!
Ω	0.70737732322703	Real period
R	1.4871331896466	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	8800a4 17600a4 79200t2 1760f4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8800u4

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 8800u4

-4	8	-3	5	-11
8800a4	17600a4	79200t2	1760f4	96800d2

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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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