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	-20842283008000 = -1 · 221 · 53 · 433	Discriminant
Eigenvalues	2- -2 5-  1 -6 -5 -6 -7	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-2305,222975]	[a1,a2,a3,a4,a6]
Generators	[-70:215:1] [-65:320:1]	Generators of the group modulo torsion
j	-5168743489/79507000	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	13760f2 3440b2 123840fe2 68800cw2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13760t2

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 13760t2

-4	8	-3	5
13760f2	3440b2	123840fe2	68800cw2

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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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