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	522j	Isogeny class
Conductor	522	Conductor
∏ cp	52	Product of Tamagawa factors cp
deg	416	Modular degree for the optimal curve
Δ	-519561216 = -1 · 213 · 37 · 29	Discriminant
Eigenvalues	2- 3- -3 -3 -6  0 -7  5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-509,4677]	[a1,a2,a3,a4,a6]
Generators	[11:12:1]	Generators of the group modulo torsion
j	-19968681097/712704	j-invariant
L	2.3288102500793	L(r)(E,1)/r!
Ω	1.6391662952835	Real period
R	0.027321701666505	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4176ba1 16704bk1 174e1 13050j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 522j1

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
-	-	-3	-3	-6	0	-7	5	8	+	-8	-3	5	3	-9	2	11	-6	0	0	-10	-2	0	-10	0

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Quadratic twists for elliptic curve 522j1

-4	8	-3	5	-7	-11	13	29
4176ba1	16704bk1	174e1	13050j1	25578bk1	63162bc1	88218t1	15138j1

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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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