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	13872z	Isogeny class
Conductor	13872	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-2.2470487555443E+19	Discriminant
Eigenvalues	2- 3+  0  1  0 -1 17-  7	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1089048,493687536]	[a1,a2,a3,a4,a6]
Generators	[-28284:593920:27]	Generators of the group modulo torsion
j	-4999353625/786432	j-invariant
L	4.2633597489608	L(r)(E,1)/r!
Ω	0.20670495005565	Real period
R	5.1563348480685	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	1734h2 55488ea2 41616cs2 13872bd2	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 13872z2

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	1	0	-1	-	7	6	0	-5	5	-12	-11	6	-12	-6	5	7	12	2	-8	6	0	-7

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Quadratic twists for elliptic curve 13872z2

-4	8	-3	17
1734h2	55488ea2	41616cs2	13872bd2

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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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