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	2	Product of Tamagawa factors cp
deg	48	Modular degree for the optimal curve
Δ	-14256 = -1 · 24 · 34 · 11	Discriminant
Eigenvalues	2+ 3+ -2 -4 11-  6  6  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,1,-6]	[a1,a2,a3,a4,a6]
j	2048/891	j-invariant
L	0.92673382967524	L(r)(E,1)/r!
Ω	1.8534676593505	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	264c1 2112y1 1584c1 13200bb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 528b1

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 528b1

-4	8	-3	5	-7	-11	13
264c1	2112y1	1584c1	13200bb1	25872x1	5808f1	89232b1

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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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