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	28896p	Isogeny class
Conductor	28896	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	77672448 = 212 · 32 · 72 · 43	Discriminant
Eigenvalues	2- 3-  2 7+ -6  2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-257,-1617]	[a1,a2,a3,a4,a6]
j	460099648/18963	j-invariant
L	2.3900593025894	L(r)(E,1)/r!
Ω	1.1950296512955	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	28896j2 57792cb1 86688m2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 28896p2

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	+	-6	2	-2	0	6	-8	-2	-2	2	-	0	-6	0	-8	-8	-8	0	16	16	6	2

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Quadratic twists for elliptic curve 28896p2

-4	8	-3
28896j2	57792cb1	86688m2

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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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