Cremona's table of elliptic curves

48672 = 2⁵ · 3² · 13²

Field	Data	Notes
Atkin-Lehner	2- 3- 13+	Signs for the Atkin-Lehner involutions
Class	48672bs	Isogeny class
Conductor	48672	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-145929341256192 = -1 · 29 · 310 · 136	Discriminant
Eigenvalues	2- 3-  2 -4 -4 13+  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,11661,320762]	[a1,a2,a3,a4,a6]
Generators	[47782:739530:343]	Generators of the group modulo torsion
j	97336/81	j-invariant
L	5.3086911118568	L(r)(E,1)/r!
Ω	0.37515467080924	Real period
R	7.075336554359	Regulator
r	1	Rank of the group of rational points
S	1.000000000005	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	48672r2 97344cj3 16224e4 288c4	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 48672bs2

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	-4	-4	+	6	-4	0	-2	4	2	2	-4	-8	-10	4	6	4	16	6	-4	-12	10	14

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Quadratic twists for elliptic curve 48672bs2

-4	8	-3	13
48672r2	97344cj3	16224e4	288c4

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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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