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	8800k	Isogeny class
Conductor	8800	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4992	Modular degree for the optimal curve
Δ	-85184000 = -1 · 29 · 53 · 113	Discriminant
Eigenvalues	2+  3 5- -3 11+  4 -7 -3	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-115,650]	[a1,a2,a3,a4,a6]
j	-2628072/1331	j-invariant
L	3.5718049667259	L(r)(E,1)/r!
Ω	1.785902483363	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	8800m1 17600dl1 79200er1 8800ba1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8800k1

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	+	4	-7	-3	0	7	3	9	-4	6	12	-7	12	1	12	9	-2	-12	12	-7	-8

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Quadratic twists for elliptic curve 8800k1

-4	8	-3	5	-11
8800m1	17600dl1	79200er1	8800ba1	96800cn1

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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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