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	528g	Isogeny class
Conductor	528	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	-522454597632 = -1 · 215 · 32 · 116	Discriminant
Eigenvalues	2- 3+  0 -2 11- -4 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-648,35568]	[a1,a2,a3,a4,a6]
Generators	[-28:176:1]	Generators of the group modulo torsion
j	-7357983625/127552392	j-invariant
L	1.7226781593617	L(r)(E,1)/r!
Ω	0.78176008867867	Real period
R	0.18363244089729	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	66a4 2112x4 1584l4 13200ck4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 528g4

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	-	-4	-6	4	-6	6	-8	-10	6	-8	6	0	0	8	4	-6	2	-14	12	-6	14

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Quadratic twists for elliptic curve 528g4

-4	8	-3	5	-7	-11	13
66a4	2112x4	1584l4	13200ck4	25872cw4	5808p4	89232y4

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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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