Cremona's table of elliptic curves

32193 = 3² · 7² · 73

Field	Data	Notes
Atkin-Lehner	3- 7- 73+	Signs for the Atkin-Lehner involutions
Class	32193c	Isogeny class
Conductor	32193	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	221184	Modular degree for the optimal curve
Δ	-295884408672307539 = -1 · 315 · 710 · 73	Discriminant
Eigenvalues	0 3- -1 7-  0 -4  1  5	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-102018,-29020973]	[a1,a2,a3,a4,a6]
Generators	[20594:1035905:8]	Generators of the group modulo torsion
j	-1369110052864/3449898459	j-invariant
L	3.7862288709074	L(r)(E,1)/r!
Ω	0.1243713872038	Real period
R	3.8053656834101	Regulator
r	1	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	10731a1 4599c1	Quadratic twists by: -3 -7

Hecke Eigenvalues for elliptic curve 32193c1

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
0	-	-1	-	0	-4	1	5	6	-6	6	1	4	-10	-9	9	-11	-3	3	8	+	-5	-3	-2	7

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Quadratic twists for elliptic curve 32193c1

-3	-7
10731a1	4599c1

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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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