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	361304064 = 212 · 36 · 112	Discriminant
Eigenvalues	2- 3- -2 -4 11+ -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-184,-364]	[a1,a2,a3,a4,a6]
Generators	[-10:24:1]	Generators of the group modulo torsion
j	169112377/88209	j-invariant
L	1.9892866004483	L(r)(E,1)/r!
Ω	1.3723166787329	Real period
R	0.48319425374544	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	33a1 2112v2 1584q2 13200bm2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 528h2

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 528h2

-4	8	-3	5	-7	-11	13
33a1	2112v2	1584q2	13200bm2	25872bk2	5808bg2	89232co2

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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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