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	32448z	Isogeny class
Conductor	32448	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	479232	Modular degree for the optimal curve
Δ	-5203983814166052864 = -1 · 222 · 32 · 1310	Discriminant
Eigenvalues	2+ 3- -1  2  2 13+  5 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-38081,-109805409]	[a1,a2,a3,a4,a6]
j	-169/144	j-invariant
L	3.4912637322144	L(r)(E,1)/r!
Ω	0.10910199163173	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32448cd1 1014d1 97344bd1 32448y1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 32448z1

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
+	-	-1	2	2	+	5	-2	6	9	4	-11	-5	-10	-2	1	-8	11	2	14	13	-4	6	-2	2

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Quadratic twists for elliptic curve 32448z1

-4	8	-3	13
32448cd1	1014d1	97344bd1	32448y1

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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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