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	528b	Isogeny class
Conductor	528	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	33792 = 210 · 3 · 11	Discriminant
Eigenvalues	2+ 3+ -2 -4 11-  6  6  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-704,-6960]	[a1,a2,a3,a4,a6]
j	37736227588/33	j-invariant
L	0.92673382967524	L(r)(E,1)/r!
Ω	0.92673382967524	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	264c4 2112y3 1584c4 13200bb3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 528b3

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

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Quadratic twists for elliptic curve 528b3

-4	8	-3	5	-7	-11	13
264c4	2112y3	1584c4	13200bb3	25872x4	5808f4	89232b4

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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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