Cremona's table of elliptic curves

47808 = 2⁶ · 3² · 83

Field	Data	Notes
Atkin-Lehner	2+ 3- 83-	Signs for the Atkin-Lehner involutions
Class	47808x	Isogeny class
Conductor	47808	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	134962681614336 = 212 · 314 · 832	Discriminant
Eigenvalues	2+ 3-  2  4  4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-80724,8810080]	[a1,a2,a3,a4,a6]
Generators	[210232:22680:1331]	Generators of the group modulo torsion
j	19482480805312/45198729	j-invariant
L	8.586557394392	L(r)(E,1)/r!
Ω	0.58484954160716	Real period
R	7.3408259591037	Regulator
r	1	Rank of the group of rational points
S	0.99999999999913	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	47808m2 23904r1 15936j2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 47808x2

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

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Quadratic twists for elliptic curve 47808x2

-4	8	-3
47808m2	23904r1	15936j2

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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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