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	13872bj	Isogeny class
Conductor	13872	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	52160495616 = 217 · 34 · 173	Discriminant
Eigenvalues	2- 3-  2 -2  0 -6 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-46472,-3871500]	[a1,a2,a3,a4,a6]
Generators	[708:17850:1]	Generators of the group modulo torsion
j	551569744601/2592	j-invariant
L	6.0025521689705	L(r)(E,1)/r!
Ω	0.32516295188081	Real period
R	4.615033888586	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	1734c2 55488cr2 41616cj2 13872w2	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 13872bj2

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	-2	0	-6	+	0	6	-6	10	-2	0	4	-8	6	0	-10	-8	10	16	-6	-16	10	-12

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Quadratic twists for elliptic curve 13872bj2

-4	8	-3	17
1734c2	55488cr2	41616cj2	13872w2

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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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