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	22176d	Isogeny class
Conductor	22176	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	344277609984 = 29 · 38 · 7 · 114	Discriminant
Eigenvalues	2+ 3- -2 7+ 11-  2  2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6411,-195550]	[a1,a2,a3,a4,a6]
Generators	[94:180:1]	Generators of the group modulo torsion
j	78073482824/922383	j-invariant
L	4.104694408774	L(r)(E,1)/r!
Ω	0.53392258490408	Real period
R	3.8439040835025	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	22176u3 44352w3 7392i3	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 22176d3

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

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Quadratic twists for elliptic curve 22176d3

-4	8	-3
22176u3	44352w3	7392i3

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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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