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	528c	Isogeny class
Conductor	528	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	672	Modular degree for the optimal curve
Δ	24634368 = 210 · 37 · 11	Discriminant
Eigenvalues	2+ 3+  4  2 11-  0 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-8016,278928]	[a1,a2,a3,a4,a6]
j	55635379958596/24057	j-invariant
L	1.7314419103037	L(r)(E,1)/r!
Ω	1.7314419103037	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	264d1 2112z1 1584e1 13200x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 528c1

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

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Quadratic twists for elliptic curve 528c1

-4	8	-3	5	-7	-11	13
264d1	2112z1	1584e1	13200x1	25872bb1	5808g1	89232e1

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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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