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	12	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	1216512 = 212 · 33 · 11	Discriminant
Eigenvalues	2- 3- -2 -4 11+ -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-104,372]	[a1,a2,a3,a4,a6]
Generators	[-2:24:1]	Generators of the group modulo torsion
j	30664297/297	j-invariant
L	1.9892866004483	L(r)(E,1)/r!
Ω	2.7446333574659	Real period
R	0.24159712687272	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	33a2 2112v1 1584q1 13200bm1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 528h1

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 528h1

-4	8	-3	5	-7	-11	13
33a2	2112v1	1584q1	13200bm1	25872bk1	5808bg1	89232co1

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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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