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	32	Product of Tamagawa factors cp
Δ	-9715064832 = -1 · 213 · 34 · 114	Discriminant
Eigenvalues	2- 3-  2  4 11- -6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-192,4788]	[a1,a2,a3,a4,a6]
j	-192100033/2371842	j-invariant
L	2.1940597109795	L(r)(E,1)/r!
Ω	1.0970298554897	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	66b4 2112u4 1584n4 13200bu4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 528j4

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 528j4

-4	8	-3	5	-7	-11	13
66b4	2112u4	1584n4	13200bu4	25872by3	5808bf4	89232cd3

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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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