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	32368o	Isogeny class
Conductor	32368	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	34560	Modular degree for the optimal curve
Δ	359356786432 = 28 · 75 · 174	Discriminant
Eigenvalues	2-  1 -2 7+  4 -4 17-  3	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3564,-77848]	[a1,a2,a3,a4,a6]
Generators	[79:374:1]	Generators of the group modulo torsion
j	234219472/16807	j-invariant
L	5.2907553042523	L(r)(E,1)/r!
Ω	0.6206775782426	Real period
R	2.841386837931	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	8092h1 129472cp1 32368bb1	Quadratic twists by: -4 8 17

Hecke Eigenvalues for elliptic curve 32368o1

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	+	4	-4	-	3	6	3	5	-10	-6	6	5	5	-3	-6	-10	14	-10	-12	5	-2	-12

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Quadratic twists for elliptic curve 32368o1

-4	8	17
8092h1	129472cp1	32368bb1

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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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