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	48672s	Isogeny class
Conductor	48672	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	632360478776832 = 29 · 39 · 137	Discriminant
Eigenvalues	2+ 3- -2  0 -4 13+  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-5695131,-5231228366]	[a1,a2,a3,a4,a6]
j	11339065490696/351	j-invariant
L	1.5636646155887	L(r)(E,1)/r!
Ω	0.097729038480582	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	16	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	48672bu4 97344bo4 16224t3 3744p2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 48672s4

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

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Quadratic twists for elliptic curve 48672s4

-4	8	-3	13
48672bu4	97344bo4	16224t3	3744p2

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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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