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	83232r	Isogeny class
Conductor	83232	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	32768	Modular degree for the optimal curve
Δ	229220928 = 26 · 36 · 173	Discriminant
Eigenvalues	2+ 3-  4  0  0 -6 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-153,0]	[a1,a2,a3,a4,a6]
j	1728	j-invariant
L	2.9821490889395	L(r)(E,1)/r!
Ω	1.4910745519544	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	83232r1 9248g1 83232u1	Quadratic twists by: -4 -3 17

Hecke Eigenvalues for elliptic curve 83232r1

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
+	-	4	0	0	-6	+	0	0	4	0	-12	8	0	0	14	0	-12	0	0	-16	0	0	10	8

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Quadratic twists for elliptic curve 83232r1

-4	-3	17
83232r1	9248g1	83232u1

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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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