Cremona's table of elliptic curves

83475 = 3² · 5² · 7 · 53

Field	Data	Notes
Atkin-Lehner	3- 5- 7+ 53-	Signs for the Atkin-Lehner involutions
Class	83475bl	Isogeny class
Conductor	83475	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	658944	Modular degree for the optimal curve
Δ	-17948369194875 = -1 · 39 · 53 · 72 · 533	Discriminant
Eigenvalues	-2 3- 5- 7+  0 -2 -1 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-279795,56965356]	[a1,a2,a3,a4,a6]
Generators	[359:1669:1] [305:-23:1]	Generators of the group modulo torsion
j	-26583124095291392/196964271	j-invariant
L	5.5104910423038	L(r)(E,1)/r!
Ω	0.61848268186697	Real period
R	0.37123722323217	Regulator
r	2	Rank of the group of rational points
S	0.9999999999819	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	27825v1 83475bp1	Quadratic twists by: -3 5

Hecke Eigenvalues for elliptic curve 83475bl1

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	-	-	+	0	-2	-1	-6	0	-10	8	2	-5	-10	-3	-	-4	-8	-13	-7	-3	10	16	6	-8

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Quadratic twists for elliptic curve 83475bl1

-3	5
27825v1	83475bp1

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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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