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	528a	Isogeny class
Conductor	528	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	33792 = 210 · 3 · 11	Discriminant
Eigenvalues	2+ 3+  0 -2 11+  0 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8,0]	[a1,a2,a3,a4,a6]
Generators	[-2:2:1]	Generators of the group modulo torsion
j	62500/33	j-invariant
L	1.7218133021209	L(r)(E,1)/r!
Ω	2.9816925530613	Real period
R	0.57746171728977	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	264a1 2112ba1 1584f1 13200q1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 528a1

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

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Quadratic twists for elliptic curve 528a1

-4	8	-3	5	-7	-11	13
264a1	2112ba1	1584f1	13200q1	25872l1	5808e1	89232g1

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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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