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	4	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	4866048 = 214 · 33 · 11	Discriminant
Eigenvalues	2- 3+  0 -2 11- -4 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-88,-272]	[a1,a2,a3,a4,a6]
Generators	[-6:2:1]	Generators of the group modulo torsion
j	18609625/1188	j-invariant
L	1.7226781593617	L(r)(E,1)/r!
Ω	1.5635201773573	Real period
R	1.1017946453837	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	66a1 2112x1 1584l1 13200ck1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 528g1

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 528g1

-4	8	-3	5	-7	-11	13
66a1	2112x1	1584l1	13200ck1	25872cw1	5808p1	89232y1

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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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