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	528d	Isogeny class
Conductor	528	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	1115136 = 210 · 32 · 112	Discriminant
Eigenvalues	2+ 3-  2  0 11+  2  6  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-32,-60]	[a1,a2,a3,a4,a6]
j	3650692/1089	j-invariant
L	2.048195850677	L(r)(E,1)/r!
Ω	2.048195850677	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	264b2 2112w2 1584g2 13200a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 528d2

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	0	+	2	6	0	-4	2	0	-10	6	8	4	-6	12	2	-4	-12	-14	-16	12	10	-14

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Quadratic twists for elliptic curve 528d2

-4	8	-3	5	-7	-11	13
264b2	2112w2	1584g2	13200a2	25872d2	5808n2	89232u2

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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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