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	32368b	Isogeny class
Conductor	32368	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	6048	Modular degree for the optimal curve
Δ	-1586032 = -1 · 24 · 73 · 172	Discriminant
Eigenvalues	2+ -2  2 7+  0 -4 17+  6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-232,1287]	[a1,a2,a3,a4,a6]
Generators	[9:3:1]	Generators of the group modulo torsion
j	-299944192/343	j-invariant
L	3.8132875897926	L(r)(E,1)/r!
Ω	2.6626789901208	Real period
R	1.4321244145242	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	16184e1 129472cd1 32368f1	Quadratic twists by: -4 8 17

Hecke Eigenvalues for elliptic curve 32368b1

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	2	+	0	-4	+	6	-3	-5	2	3	0	-7	0	-1	14	-2	-4	11	-4	5	4	8	-2

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Quadratic twists for elliptic curve 32368b1

-4	8	17
16184e1	129472cd1	32368f1

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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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