Cremona's table of elliptic curves

528 = 2⁴ · 3 · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 11+	Signs for the Atkin-Lehner involutions
Class	528h	Isogeny class
Conductor	528	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	-23944605696 = -1 · 212 · 312 · 11	Discriminant
Eigenvalues	2- 3- -2 -4 11+ -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,696,-2124]	[a1,a2,a3,a4,a6]
Generators	[6:48:1]	Generators of the group modulo torsion
j	9090072503/5845851	j-invariant
L	1.9892866004483	L(r)(E,1)/r!
Ω	0.68615833936647	Real period
R	0.96638850749087	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	33a4 2112v4 1584q4 13200bm4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 528h4

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	-4	+	-2	-2	0	-8	-6	8	6	-2	0	-8	6	4	6	4	0	-14	4	-12	-6	2

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Quadratic twists for elliptic curve 528h4

-4	8	-3	5	-7	-11	13
33a4	2112v4	1584q4	13200bm4	25872bk3	5808bg4	89232co3

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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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