Cremona's table of elliptic curves

8052 = 2² · 3 · 11 · 61

Field	Data	Notes
Atkin-Lehner	2- 3+ 11- 61+	Signs for the Atkin-Lehner involutions
Class	8052a	Isogeny class
Conductor	8052	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	8736	Modular degree for the optimal curve
Δ	564849507024 = 24 · 314 · 112 · 61	Discriminant
Eigenvalues	2- 3+ -2  2 11-  2  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3189,-58086]	[a1,a2,a3,a4,a6]
Generators	[-2012:6435:64]	Generators of the group modulo torsion
j	224235033198592/35303094189	j-invariant
L	3.4450601743671	L(r)(E,1)/r!
Ω	0.64203796246018	Real period
R	5.3658200539516	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	32208n1 128832q1 24156e1 88572c1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 8052a1

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

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Quadratic twists for elliptic curve 8052a1

-4	8	-3	-11
32208n1	128832q1	24156e1	88572c1

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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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