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	13872bl	Isogeny class
Conductor	13872	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	54432	Modular degree for the optimal curve
Δ	-11929412173824 = -1 · 221 · 39 · 172	Discriminant
Eigenvalues	2- 3-  3 -4  3  2 17+ -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-25664,1582644]	[a1,a2,a3,a4,a6]
Generators	[10:1152:1]	Generators of the group modulo torsion
j	-1579268174113/10077696	j-invariant
L	6.4911894272366	L(r)(E,1)/r!
Ω	0.71812883453731	Real period
R	0.25108421880791	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	1734j1 55488cx1 41616cp1 13872bb1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 13872bl1

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
-	-	3	-4	3	2	+	-8	6	-3	-7	-8	-6	4	6	-9	-15	-14	-2	0	7	-1	-12	0	13

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Quadratic twists for elliptic curve 13872bl1

-4	8	-3	17
1734j1	55488cx1	41616cp1	13872bb1

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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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