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	13872bk	Isogeny class
Conductor	13872	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	2160	Modular degree for the optimal curve
Δ	-1123632 = -1 · 24 · 35 · 172	Discriminant
Eigenvalues	2- 3-  2  3 -4  1 17+ -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,23,-22]	[a1,a2,a3,a4,a6]
Generators	[2:6:1]	Generators of the group modulo torsion
j	278528/243	j-invariant
L	6.9025452874705	L(r)(E,1)/r!
Ω	1.5138698841358	Real period
R	0.91190733890725	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	3468c1 55488cs1 41616ck1 13872ba1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 13872bk1

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	3	-4	1	+	-7	-6	-8	5	5	-4	-9	0	0	12	1	-15	6	-10	-8	-10	18	-13

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Quadratic twists for elliptic curve 13872bk1

-4	8	-3	17
3468c1	55488cs1	41616ck1	13872ba1

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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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