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	528j	Isogeny class
Conductor	528	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	270336 = 213 · 3 · 11	Discriminant
Eigenvalues	2- 3-  2  4 11- -6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-5632,160820]	[a1,a2,a3,a4,a6]
j	4824238966273/66	j-invariant
L	2.1940597109795	L(r)(E,1)/r!
Ω	2.1940597109795	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	66b3 2112u3 1584n3 13200bu3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 528j3

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

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Quadratic twists for elliptic curve 528j3

-4	8	-3	5	-7	-11	13
66b3	2112u3	1584n3	13200bu3	25872by4	5808bf3	89232cd4

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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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