Cremona's table of elliptic curves

22176 = 2⁵ · 3² · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 11-	Signs for the Atkin-Lehner involutions
Class	22176p	Isogeny class
Conductor	22176	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-639055031763456 = -1 · 29 · 39 · 78 · 11	Discriminant
Eigenvalues	2- 3- -2 7+ 11- -2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,21309,214090]	[a1,a2,a3,a4,a6]
Generators	[134:2340:1] [890:26910:1]	Generators of the group modulo torsion
j	2866919053816/1712145897	j-invariant
L	6.8747281286591	L(r)(E,1)/r!
Ω	0.3134015671019	Real period
R	21.935844776502	Regulator
r	2	Rank of the group of rational points
S	0.9999999999999	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	22176f2 44352v3 7392c4	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 22176p2

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	-6	0	-8	-6	-4	-2	-6	-8	-8	-2	-4	-2	-12	0	10	0	-4	14	2

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Quadratic twists for elliptic curve 22176p2

-4	8	-3
22176f2	44352v3	7392c4

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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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