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	32448de	Isogeny class
Conductor	32448	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	159744	Modular degree for the optimal curve
Δ	-4330238011047936 = -1 · 216 · 34 · 138	Discriminant
Eigenvalues	2- 3- -3  0  0 13+ -1  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,32223,-2240289]	[a1,a2,a3,a4,a6]
Generators	[225:4056:1]	Generators of the group modulo torsion
j	69212/81	j-invariant
L	5.0957525806318	L(r)(E,1)/r!
Ω	0.23499211986205	Real period
R	0.90353252831472	Regulator
r	1	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32448j1 8112c1 97344fp1 32448db1	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 32448de1

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
-	-	-3	0	0	+	-1	0	-4	-3	-8	5	3	4	8	13	12	-15	12	-8	3	4	12	10	2

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Quadratic twists for elliptic curve 32448de1

-4	8	-3	13
32448j1	8112c1	97344fp1	32448db1

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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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