Cremona's table of elliptic curves

83520 = 2⁶ · 3² · 5 · 29

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 29-	Signs for the Atkin-Lehner involutions
Class	83520gj	Isogeny class
Conductor	83520	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	73728	Modular degree for the optimal curve
Δ	-14612659200 = -1 · 210 · 39 · 52 · 29	Discriminant
Eigenvalues	2- 3- 5-  3 -5  5  3 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-12,-5816]	[a1,a2,a3,a4,a6]
Generators	[29:135:1]	Generators of the group modulo torsion
j	-256/19575	j-invariant
L	8.2417820380375	L(r)(E,1)/r!
Ω	0.5705227272593	Real period
R	1.8057523483225	Regulator
r	1	Rank of the group of rational points
S	1.000000000228	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	83520db1 20880k1 27840dj1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 83520gj1

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
-	-	-	3	-5	5	3	-8	4	-	4	-4	10	-10	-5	8	-8	10	-13	14	-12	4	-16	-1	-16

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Quadratic twists for elliptic curve 83520gj1

-4	8	-3
83520db1	20880k1	27840dj1

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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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