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
deg	3072	Modular degree for the optimal curve
Δ	3025000000 = 26 · 58 · 112	Discriminant
Eigenvalues	2-  0 5+  0 11-  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-925,10500]	[a1,a2,a3,a4,a6]
Generators	[64:462:1]	Generators of the group modulo torsion
j	87528384/3025	j-invariant
L	4.2078571798972	L(r)(E,1)/r!
Ω	1.4147546464541	Real period
R	2.9742663792933	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	8800a1 17600a2 79200t1 1760f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8800u1

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 8800u1

-4	8	-3	5	-11
8800a1	17600a2	79200t1	1760f1	96800d1

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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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