Cremona's table of elliptic curves

83232 = 2⁵ · 3² · 17²

Field	Data	Notes
Atkin-Lehner	2+ 3- 17+	Signs for the Atkin-Lehner involutions
Class	83232j	Isogeny class
Conductor	83232	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1378422801179136 = 29 · 38 · 177	Discriminant
Eigenvalues	2+ 3-  2  0 -4 -2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4245699,3367222810]	[a1,a2,a3,a4,a6]
j	939464338184/153	j-invariant
L	0.75453673797347	L(r)(E,1)/r!
Ω	0.37726838873736	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	83232i4 27744z4 4896b3	Quadratic twists by: -4 -3 17

Hecke Eigenvalues for elliptic curve 83232j4

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

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Quadratic twists for elliptic curve 83232j4

-4	-3	17
83232i4	27744z4	4896b3

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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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