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	16	Product of Tamagawa factors cp
Δ	-14670139392 = -1 · 212 · 36 · 173	Discriminant
Eigenvalues	2+ 3-  4  0  0 -6 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,612,0]	[a1,a2,a3,a4,a6]
j	1728	j-invariant
L	2.9821490889395	L(r)(E,1)/r!
Ω	0.7455372759772	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	83232r2 9248g2 83232u2	Quadratic twists by: -4 -3 17

Hecke Eigenvalues for elliptic curve 83232r2

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 83232r2

-4	-3	17
83232r2	9248g2	83232u2

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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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