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	13872bf	Isogeny class
Conductor	13872	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-132031254528 = -1 · 212 · 38 · 173	Discriminant
Eigenvalues	2- 3-  0  4 -4  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,992,-12364]	[a1,a2,a3,a4,a6]
Generators	[20:126:1]	Generators of the group modulo torsion
j	5359375/6561	j-invariant
L	6.4306737529826	L(r)(E,1)/r!
Ω	0.55724759310431	Real period
R	1.4425081939696	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	867b2 55488ce2 41616by2 13872r2	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 13872bf2

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

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Quadratic twists for elliptic curve 13872bf2

-4	8	-3	17
867b2	55488ce2	41616by2	13872r2

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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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