Cremona's table of elliptic curves

6832 = 2⁴ · 7 · 61

Field	Data	Notes
Atkin-Lehner	2- 7+ 61-	Signs for the Atkin-Lehner involutions
Class	6832h	Isogeny class
Conductor	6832	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-406749952 = -1 · 28 · 7 · 613	Discriminant
Eigenvalues	2-  2  0 7+ -6  2  3  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1093,14313]	[a1,a2,a3,a4,a6]
Generators	[57:366:1]	Generators of the group modulo torsion
j	-564600832000/1588867	j-invariant
L	5.3678388469858	L(r)(E,1)/r!
Ω	1.6888426728124	Real period
R	0.52973543494204	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1708b2 27328r2 61488bc2 47824n2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 6832h2

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	+	-6	2	3	4	6	-6	-5	8	0	4	-12	-12	-9	-	-14	-6	14	-2	6	6	-10

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Quadratic twists for elliptic curve 6832h2

-4	8	-3	-7
1708b2	27328r2	61488bc2	47824n2

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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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