Cremona's table of elliptic curves

32368 = 2⁴ · 7 · 17²

Field	Data	Notes
Atkin-Lehner	2- 7+ 17-	Signs for the Atkin-Lehner involutions
Class	32368n	Isogeny class
Conductor	32368	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	117504	Modular degree for the optimal curve
Δ	3200142677573632 = 216 · 7 · 178	Discriminant
Eigenvalues	2-  1 -2 7+ -2  2 17-  3	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-67144,-6141068]	[a1,a2,a3,a4,a6]
Generators	[-966:3757:8]	Generators of the group modulo torsion
j	1171657/112	j-invariant
L	4.9478377016725	L(r)(E,1)/r!
Ω	0.29840370110764	Real period
R	2.7635033140824	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	4046g1 129472co1 32368ba1	Quadratic twists by: -4 8 17

Hecke Eigenvalues for elliptic curve 32368n1

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
-	1	-2	+	-2	2	-	3	0	3	5	2	0	0	-7	-7	-3	6	14	-16	-4	0	-7	10	18

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Quadratic twists for elliptic curve 32368n1

-4	8	17
4046g1	129472co1	32368ba1

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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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