Cremona's table of elliptic curves

13872 = 2⁴ · 3 · 17²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 17+	Signs for the Atkin-Lehner involutions
Class	13872a	Isogeny class
Conductor	13872	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1728	Modular degree for the optimal curve
Δ	-1997568 = -1 · 28 · 33 · 172	Discriminant
Eigenvalues	2+ 3+  0 -3  2 -3 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-28,-80]	[a1,a2,a3,a4,a6]
Generators	[8:12:1]	Generators of the group modulo torsion
j	-34000/27	j-invariant
L	3.423835739058	L(r)(E,1)/r!
Ω	1.0005868461619	Real period
R	1.7109138263166	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6936l1 55488dh1 41616u1 13872q1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 13872a1

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
+	+	0	-3	2	-3	+	-1	4	6	7	-11	-6	1	8	4	6	-3	-5	0	-2	-4	8	-2	3

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Quadratic twists for elliptic curve 13872a1

-4	8	-3	17
6936l1	55488dh1	41616u1	13872q1

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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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