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	13872bm	Isogeny class
Conductor	13872	Conductor
∏ cp	10	Product of Tamagawa factors cp
Δ	-118033833938006016 = -1 · 212 · 35 · 179	Discriminant
Eigenvalues	2- 3- -3 -2  5 -1 17+  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-3904197,2967987699]	[a1,a2,a3,a4,a6]
Generators	[1830:44217:1]	Generators of the group modulo torsion
j	-13549359104/243	j-invariant
L	4.5749240819984	L(r)(E,1)/r!
Ω	0.30489289536921	Real period
R	1.5005020292318	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	867c2 55488cu2 41616cm2 13872x2	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 13872bm2

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	-2	5	-1	+	5	1	-6	-10	-2	-5	-1	2	6	0	10	12	0	6	4	-6	-10	8

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Quadratic twists for elliptic curve 13872bm2

-4	8	-3	17
867c2	55488cu2	41616cm2	13872x2

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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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