Cremona's table of elliptic curves

28896 = 2⁵ · 3 · 7 · 43

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 43+	Signs for the Atkin-Lehner involutions
Class	28896o	Isogeny class
Conductor	28896	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	11264	Modular degree for the optimal curve
Δ	2557122624 = 26 · 32 · 74 · 432	Discriminant
Eigenvalues	2- 3- -2 7+  0 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-714,6696]	[a1,a2,a3,a4,a6]
Generators	[356:6708:1]	Generators of the group modulo torsion
j	629863565248/39955041	j-invariant
L	5.1913304731833	L(r)(E,1)/r!
Ω	1.4189762320306	Real period
R	3.6585041778707	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	28896f1 57792j2 86688i1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 28896o1

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	+	0	-2	2	-4	0	6	-4	2	-6	+	8	6	0	-6	4	8	-6	12	16	6	2

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Quadratic twists for elliptic curve 28896o1

-4	8	-3
28896f1	57792j2	86688i1

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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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