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	128	Product of Tamagawa factors cp
Δ	57838638477312 = 212 · 39 · 72 · 114	Discriminant
Eigenvalues	2- 3- -2 7+ 11- -2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-64956,6361504]	[a1,a2,a3,a4,a6]
Generators	[-244:2772:1] [-211:3267:1]	Generators of the group modulo torsion
j	10150654719808/19370043	j-invariant
L	6.8747281286591	L(r)(E,1)/r!
Ω	0.62680313420381	Real period
R	1.3709902985314	Regulator
r	2	Rank of the group of rational points
S	0.9999999999999	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	22176f4 44352v1 7392c2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 22176p4

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 22176p4

-4	8	-3
22176f4	44352v1	7392c2

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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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