Cremona's table of elliptic curves

13760 = 2⁶ · 5 · 43

Field	Data	Notes
Atkin-Lehner	2- 5- 43-	Signs for the Atkin-Lehner involutions
Class	13760t	Isogeny class
Conductor	13760	Conductor
∏ cp	36	Product of Tamagawa factors cp
Δ	-44032000000000 = -1 · 219 · 59 · 43	Discriminant
Eigenvalues	2- -2 5-  1 -6 -5 -6 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-360065,83041663]	[a1,a2,a3,a4,a6]
Generators	[31:8480:1] [293:1668:1]	Generators of the group modulo torsion
j	-19693718244927649/167968750	j-invariant
L	5.0988564922574	L(r)(E,1)/r!
Ω	0.57632177649442	Real period
R	0.24575663863371	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	13760f3 3440b3 123840fe3 68800cw3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13760t3

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
-	-2	-	1	-6	-5	-6	-7	6	3	-5	-2	-3	-	-12	-6	-12	1	-13	-12	11	1	0	6	8

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Quadratic twists for elliptic curve 13760t3

-4	8	-3	5
13760f3	3440b3	123840fe3	68800cw3

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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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