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	32448g	Isogeny class
Conductor	32448	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	20818451976192 = 212 · 34 · 137	Discriminant
Eigenvalues	2+ 3+ -2 -2 -6 13+ -2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-9689,297465]	[a1,a2,a3,a4,a6]
Generators	[152:-1521:1]	Generators of the group modulo torsion
j	5088448/1053	j-invariant
L	2.1359298539006	L(r)(E,1)/r!
Ω	0.64519752737845	Real period
R	0.82762633273681	Regulator
r	1	Rank of the group of rational points
S	1.0000000000001	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	32448bl2 16224j1 97344bw2 2496e2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 32448g2

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
+	+	-2	-2	-6	+	-2	-6	0	6	-6	2	10	-8	-6	-6	-6	10	2	14	14	4	6	-6	14

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Quadratic twists for elliptic curve 32448g2

-4	8	-3	13
32448bl2	16224j1	97344bw2	2496e2

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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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