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	32368bd	Isogeny class
Conductor	32368	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	93053283705847808 = 215 · 76 · 176	Discriminant
Eigenvalues	2- -2  0 7-  0 -4 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-164248,20946324]	[a1,a2,a3,a4,a6]
Generators	[28:4046:1]	Generators of the group modulo torsion
j	4956477625/941192	j-invariant
L	3.2558896792685	L(r)(E,1)/r!
Ω	0.32147884629658	Real period
R	0.84398753779509	Regulator
r	1	Rank of the group of rational points
S	0.99999999999996	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4046b4 129472de4 112c4	Quadratic twists by: -4 8 17

Hecke Eigenvalues for elliptic curve 32368bd4

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	-	0	-4	+	-2	0	6	-4	-2	-6	-8	12	6	6	-8	4	0	-2	8	6	-6	10

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Quadratic twists for elliptic curve 32368bd4

-4	8	17
4046b4	129472de4	112c4

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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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