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	8800z	Isogeny class
Conductor	8800	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	4608	Modular degree for the optimal curve
Δ	605000000 = 26 · 57 · 112	Discriminant
Eigenvalues	2-  2 5+  4 11- -4 -4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-258,-988]	[a1,a2,a3,a4,a6]
Generators	[32:150:1]	Generators of the group modulo torsion
j	1906624/605	j-invariant
L	6.5312288998019	L(r)(E,1)/r!
Ω	1.2206433819319	Real period
R	1.337661145851	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	8800t1 17600by2 79200be1 1760h1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8800z1

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

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Quadratic twists for elliptic curve 8800z1

-4	8	-3	5	-11
8800t1	17600by2	79200be1	1760h1	96800u1

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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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