Cremona's table of elliptic curves

32448 = 2⁶ · 3 · 13²

Field	Data	Notes
Atkin-Lehner	2- 3- 13-	Signs for the Atkin-Lehner involutions
Class	32448dp	Isogeny class
Conductor	32448	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	14073273535905792 = 214 · 34 · 139	Discriminant
Eigenvalues	2- 3- -4 -2 -2 13-  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3799345,-2851696561]	[a1,a2,a3,a4,a6]
j	34909201168/81	j-invariant
L	1.7301844536084	L(r)(E,1)/r!
Ω	0.10813652835089	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	32448v2 8112h2 97344gq2 32448do2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 32448dp2

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
-	-	-4	-2	-2	-	6	2	8	-6	10	-4	0	4	-2	10	14	2	2	-6	8	0	-6	0	0

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Quadratic twists for elliptic curve 32448dp2

-4	8	-3	13
32448v2	8112h2	97344gq2	32448do2

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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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