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	13872l	Isogeny class
Conductor	13872	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	220320	Modular degree for the optimal curve
Δ	-111476398719227904 = -1 · 211 · 33 · 1710	Discriminant
Eigenvalues	2+ 3- -1  4  3  2 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1364176,-613938124]	[a1,a2,a3,a4,a6]
j	-68001122/27	j-invariant
L	3.7716844171576	L(r)(E,1)/r!
Ω	0.069846007725141	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	9	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6936g1 55488ci1 41616v1 13872f1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 13872l1

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
+	-	-1	4	3	2	+	0	6	1	5	0	-6	-4	6	-13	-7	10	14	8	-1	11	4	8	13

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Quadratic twists for elliptic curve 13872l1

-4	8	-3	17
6936g1	55488ci1	41616v1	13872f1

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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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