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	13872h	Isogeny class
Conductor	13872	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	24480	Modular degree for the optimal curve
Δ	-334836357168 = -1 · 24 · 3 · 178	Discriminant
Eigenvalues	2+ 3+ -4  1  2 -3 17-  5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3275,78426]	[a1,a2,a3,a4,a6]
j	-34816/3	j-invariant
L	0.94151702091326	L(r)(E,1)/r!
Ω	0.94151702091326	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6936q1 55488ej1 41616bh1 13872o1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 13872h1

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
+	+	-4	1	2	-3	-	5	4	-6	-5	-5	6	11	-4	12	-2	-5	9	12	-14	4	-16	18	-3

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Quadratic twists for elliptic curve 13872h1

-4	8	-3	17
6936q1	55488ej1	41616bh1	13872o1

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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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