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	32448w	Isogeny class
Conductor	32448	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-40094796398592 = -1 · 214 · 3 · 138	Discriminant
Eigenvalues	2+ 3-  0  4 -2 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,7887,-139281]	[a1,a2,a3,a4,a6]
j	686000/507	j-invariant
L	2.8945763293162	L(r)(E,1)/r!
Ω	0.36182204116444	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	32448bz2 4056k2 97344z2 2496m2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 32448w2

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

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Quadratic twists for elliptic curve 32448w2

-4	8	-3	13
32448bz2	4056k2	97344z2	2496m2

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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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