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	13872ba	Isogeny class
Conductor	13872	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	36720	Modular degree for the optimal curve
Δ	-27121744930608 = -1 · 24 · 35 · 178	Discriminant
Eigenvalues	2- 3+ -2 -3  4  1 17- -7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,6551,-147572]	[a1,a2,a3,a4,a6]
Generators	[9624:185786:27]	Generators of the group modulo torsion
j	278528/243	j-invariant
L	3.0053922469929	L(r)(E,1)/r!
Ω	0.36716737857256	Real period
R	8.1853465813794	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	3468h1 55488ef1 41616cu1 13872bk1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 13872ba1

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 13872ba1

-4	8	-3	17
3468h1	55488ef1	41616cu1	13872bk1

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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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