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	32448bw	Isogeny class
Conductor	32448	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	13440	Modular degree for the optimal curve
Δ	-444180672 = -1 · 26 · 35 · 134	Discriminant
Eigenvalues	2- 3+  0 -1  6 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-563,5433]	[a1,a2,a3,a4,a6]
j	-10816000/243	j-invariant
L	1.66972165799	L(r)(E,1)/r!
Ω	1.6697216579875	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32448cv1 16224r1 97344ek1 32448bv1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 32448bw1

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	-1	6	+	2	-4	-4	0	5	6	12	-7	2	-12	-4	-11	13	-8	1	3	6	-6	-3

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Quadratic twists for elliptic curve 32448bw1

-4	8	-3	13
32448cv1	16224r1	97344ek1	32448bv1

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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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