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	13872b	Isogeny class
Conductor	13872	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-324334776748032 = -1 · 211 · 38 · 176	Discriminant
Eigenvalues	2+ 3+  2  0  4 -2 17+  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,4528,856992]	[a1,a2,a3,a4,a6]
Generators	[-62:578:1]	Generators of the group modulo torsion
j	207646/6561	j-invariant
L	4.8810809957928	L(r)(E,1)/r!
Ω	0.40885451595969	Real period
R	1.4923037429144	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	6936m6 55488du5 41616x5 48a6	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 13872b6

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

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Quadratic twists for elliptic curve 13872b6

-4	8	-3	17
6936m6	55488du5	41616x5	48a6

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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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