Cremona's table of elliptic curves

21056 = 2⁶ · 7 · 47

Field	Data	Notes
Atkin-Lehner	2- 7- 47+	Signs for the Atkin-Lehner involutions
Class	21056ba	Isogeny class
Conductor	21056	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	226997829632 = 221 · 72 · 472	Discriminant
Eigenvalues	2-  2 -2 7- -2 -2  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3169,65793]	[a1,a2,a3,a4,a6]
Generators	[-24:357:1]	Generators of the group modulo torsion
j	13430356633/865928	j-invariant
L	6.4500646983203	L(r)(E,1)/r!
Ω	0.97603184520273	Real period
R	3.3042286120186	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	21056h2 5264k2	Quadratic twists by: -4 8

Hecke Eigenvalues for elliptic curve 21056ba2

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	-2	-	-2	-2	6	4	-8	4	-8	10	6	2	+	14	-6	0	-14	-16	-2	16	14	-6	-2

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Quadratic twists for elliptic curve 21056ba2

-4	8
21056h2	5264k2

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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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