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	13872p	Isogeny class
Conductor	13872	Conductor
∏ cp	36	Product of Tamagawa factors cp
deg	15552	Modular degree for the optimal curve
Δ	-5824908288 = -1 · 210 · 39 · 172	Discriminant
Eigenvalues	2+ 3- -4 -5  0 -1 17+  3	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,40,3684]	[a1,a2,a3,a4,a6]
Generators	[-14:24:1] [-8:54:1]	Generators of the group modulo torsion
j	23324/19683	j-invariant
L	5.8785625734638	L(r)(E,1)/r!
Ω	1.0526757034688	Real period
R	0.15512223211795	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	6936j1 55488cz1 41616bb1 13872g1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 13872p1

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	-5	0	-1	+	3	-6	-8	-7	3	-12	-7	-6	-4	-10	-5	-13	8	-10	8	-2	-4	-17

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Quadratic twists for elliptic curve 13872p1

-4	8	-3	17
6936j1	55488cz1	41616bb1	13872g1

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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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