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	522l	Isogeny class
Conductor	522	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	56	Modular degree for the optimal curve
Δ	-84564 = -1 · 22 · 36 · 29	Discriminant
Eigenvalues	2- 3-  3 -2  1  3  4 -8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-11,-17]	[a1,a2,a3,a4,a6]
j	-185193/116	j-invariant
L	2.5676032368489	L(r)(E,1)/r!
Ω	1.2838016184244	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4176bg1 16704bb1 58a1 13050m1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 522l1

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	-2	1	3	4	-8	0	-	3	-8	2	7	-11	-1	4	4	-4	2	-12	-7	0	6	-6

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Quadratic twists for elliptic curve 522l1

-4	8	-3	5	-7	-11	13	29
4176bg1	16704bb1	58a1	13050m1	25578bw1	63162x1	88218bd1	15138h1

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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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