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	528f	Isogeny class
Conductor	528	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	480	Modular degree for the optimal curve
Δ	11211374592 = 222 · 35 · 11	Discriminant
Eigenvalues	2- 3+ -4  2 11+  4 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-720,-5184]	[a1,a2,a3,a4,a6]
j	10091699281/2737152	j-invariant
L	0.94027960528629	L(r)(E,1)/r!
Ω	0.94027960528629	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	66c1 2112bd1 1584s1 13200cf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 528f1

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

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Quadratic twists for elliptic curve 528f1

-4	8	-3	5	-7	-11	13
66c1	2112bd1	1584s1	13200cf1	25872cs1	5808v1	89232br1

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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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