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	528f	Isogeny class
Conductor	528	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-1912314440982528 = -1 · 213 · 32 · 1110	Discriminant
Eigenvalues	2- 3+ -4  2 11+  4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-160880,24979776]	[a1,a2,a3,a4,a6]
j	-112427521449300721/466873642818	j-invariant
L	0.94027960528629	L(r)(E,1)/r!
Ω	0.47013980264314	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	66c4 2112bd4 1584s4 13200cf4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 528f4

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
-	+	-4	2	+	4	-2	0	6	10	8	-2	2	-4	2	4	0	-8	12	-2	-6	-10	-4	10	-2

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Quadratic twists for elliptic curve 528f4

-4	8	-3	5	-7	-11	13
66c4	2112bd4	1584s4	13200cf4	25872cs4	5808v4	89232br4

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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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