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	22176x	Isogeny class
Conductor	22176	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	2489610816 = 26 · 38 · 72 · 112	Discriminant
Eigenvalues	2- 3-  2 7- 11- -2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-1389,19780]	[a1,a2,a3,a4,a6]
Generators	[32:90:1]	Generators of the group modulo torsion
j	6352182208/53361	j-invariant
L	6.3156906470668	L(r)(E,1)/r!
Ω	1.4545953025995	Real period
R	2.1709442605033	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	22176b1 44352cb2 7392f1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 22176x1

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	4	0	-6	-8	-10	-2	0	12	6	4	14	-4	0	-10	8	-16	6	2

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Quadratic twists for elliptic curve 22176x1

-4	8	-3
22176b1	44352cb2	7392f1

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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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