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	32448c	Isogeny class
Conductor	32448	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-27104082365448192 = -1 · 216 · 3 · 1310	Discriminant
Eigenvalues	2+ 3+  2  0  0 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,5183,-7921343]	[a1,a2,a3,a4,a6]
Generators	[262239120:-10408260127:166375]	Generators of the group modulo torsion
j	48668/85683	j-invariant
L	5.3878174307319	L(r)(E,1)/r!
Ω	0.17431653119718	Real period
R	15.454120712847	Regulator
r	1	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	32448da3 4056f4 97344by3 2496c4	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 32448c3

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	0	0	+	2	-4	0	-6	0	-2	-6	12	4	-6	-8	2	4	12	14	0	8	18	6

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Quadratic twists for elliptic curve 32448c3

-4	8	-3	13
32448da3	4056f4	97344by3	2496c4

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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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