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	32368k	Isogeny class
Conductor	32368	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	137206117300969472 = 213 · 74 · 178	Discriminant
Eigenvalues	2-  2  0 7+ -2 -2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-129568,-2111616]	[a1,a2,a3,a4,a6]
j	2433138625/1387778	j-invariant
L	2.1782832129305	L(r)(E,1)/r!
Ω	0.27228540161684	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4046q2 129472cf2 1904e2	Quadratic twists by: -4 8 17

Hecke Eigenvalues for elliptic curve 32368k2

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	0	+	-2	-2	+	0	4	-4	0	-8	2	0	0	2	-4	12	8	12	14	12	-4	-6	-6

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Quadratic twists for elliptic curve 32368k2

-4	8	17
4046q2	129472cf2	1904e2

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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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