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	32368s	Isogeny class
Conductor	32368	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	36720	Modular degree for the optimal curve
Δ	-781284833392 = -1 · 24 · 7 · 178	Discriminant
Eigenvalues	2-  2  2 7+  0  4 17- -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,1638,-34573]	[a1,a2,a3,a4,a6]
Generators	[221191:361539:12167]	Generators of the group modulo torsion
j	4352/7	j-invariant
L	9.10620563655	L(r)(E,1)/r!
Ω	0.47267803479035	Real period
R	6.421711303332	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	8092i1 129472cr1 32368be1	Quadratic twists by: -4 8 17

Hecke Eigenvalues for elliptic curve 32368s1

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	1	-7	-6	1	4	-1	-4	3	-2	10	4	-1	-8	9	0	16	-6

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Quadratic twists for elliptic curve 32368s1

-4	8	17
8092i1	129472cr1	32368be1

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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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