Cremona's table of elliptic curves

52022 = 2 · 19 · 37²

Field	Data	Notes
Atkin-Lehner	2- 19+ 37+	Signs for the Atkin-Lehner involutions
Class	52022i	Isogeny class
Conductor	52022	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	103680	Modular degree for the optimal curve
Δ	-389990414168 = -1 · 23 · 19 · 376	Discriminant
Eigenvalues	2-  1  0 -1 -6 -5 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-21248,1190744]	[a1,a2,a3,a4,a6]
Generators	[-34:1386:1] [838:2319:8]	Generators of the group modulo torsion
j	-413493625/152	j-invariant
L	14.737733916453	L(r)(E,1)/r!
Ω	0.93245407190815	Real period
R	1.3171099038957	Regulator
r	2	Rank of the group of rational points
S	0.99999999999977	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	38a3	Quadratic twists by: 37

Hecke Eigenvalues for elliptic curve 52022i1

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
-	1	0	-1	-6	-5	-3	+	-3	-9	4	+	0	-8	0	-3	-9	10	5	-6	-7	10	-6	12	10

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Quadratic twists for elliptic curve 52022i1

37
38a3

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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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