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	13872bc	Isogeny class
Conductor	13872	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	12096	Modular degree for the optimal curve
Δ	-4105224192 = -1 · 214 · 3 · 174	Discriminant
Eigenvalues	2- 3+  4 -3  4 -5 17- -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-96,-3072]	[a1,a2,a3,a4,a6]
Generators	[32:160:1]	Generators of the group modulo torsion
j	-289/12	j-invariant
L	4.8580284260095	L(r)(E,1)/r!
Ω	0.60689876358072	Real period
R	2.0011691889711	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	1734m1 55488ek1 41616cx1 13872bo1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 13872bc1

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
-	+	4	-3	4	-5	-	-1	-6	-4	7	1	-8	-3	6	12	6	-7	-9	0	-14	8	2	0	1

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Quadratic twists for elliptic curve 13872bc1

-4	8	-3	17
1734m1	55488ek1	41616cx1	13872bo1

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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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