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	32448cv	Isogeny class
Conductor	32448	Conductor
∏ cp	5	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]
Generators	[46:261:1]	Generators of the group modulo torsion
j	-10816000/243	j-invariant
L	6.795589395841	L(r)(E,1)/r!
Ω	0.48932895881385	Real period
R	2.7775136841742	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32448bw1 16224m1 97344ej1 32448cw1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 32448cv1

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 32448cv1

-4	8	-3	13
32448bw1	16224m1	97344ej1	32448cw1

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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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