Cremona's table of elliptic curves

522 = 2 · 3² · 29

Field	Data	Notes
Atkin-Lehner	2- 3- 29-	Signs for the Atkin-Lehner involutions
Class	522k	Isogeny class
Conductor	522	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	22071204 = 22 · 38 · 292	Discriminant
Eigenvalues	2- 3- -2  0  4  6  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-176,911]	[a1,a2,a3,a4,a6]
j	822656953/30276	j-invariant
L	2.1298310269397	L(r)(E,1)/r!
Ω	2.1298310269397	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	4176bf2 16704t2 174d2 13050l2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 522k2

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	0	4	6	2	4	0	-	-4	-6	-6	-12	8	6	-8	10	-4	8	2	4	0	-14	18

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Quadratic twists for elliptic curve 522k2

-4	8	-3	5	-7	-11	13	29
4176bf2	16704t2	174d2	13050l2	25578bu2	63162v2	88218ba2	15138g2

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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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