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	13872c	Isogeny class
Conductor	13872	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	138240	Modular degree for the optimal curve
Δ	-236887347278359296 = -1 · 28 · 33 · 1711	Discriminant
Eigenvalues	2+ 3+ -3  0 -1  3 17+ -1	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,147583,8444109]	[a1,a2,a3,a4,a6]
Generators	[80436:4426613:27]	Generators of the group modulo torsion
j	57530252288/38336139	j-invariant
L	3.0557551608835	L(r)(E,1)/r!
Ω	0.19657200353965	Real period
R	3.8863051526397	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	6936n1 55488dx1 41616z1 816d1	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 13872c1

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	0	-1	3	+	-1	7	-6	-2	4	-9	1	-10	-2	6	12	4	-12	10	2	14	4	-12

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Quadratic twists for elliptic curve 13872c1

-4	8	-3	17
6936n1	55488dx1	41616z1	816d1

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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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