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	13760b	Isogeny class
Conductor	13760	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1408	Modular degree for the optimal curve
Δ	-68800 = -1 · 26 · 52 · 43	Discriminant
Eigenvalues	2+ -2 5+ -2 -1  7  3 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,9,-5]	[a1,a2,a3,a4,a6]
Generators	[2:5:1]	Generators of the group modulo torsion
j	1124864/1075	j-invariant
L	2.5842517646556	L(r)(E,1)/r!
Ω	1.8951843008484	Real period
R	0.6817943150697	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	13760c1 6880e1 123840cr1 68800bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13760b1

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	+	-2	-1	7	3	-6	-5	-6	-7	10	5	+	-4	-1	8	8	3	8	-8	8	9	6	-15

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Quadratic twists for elliptic curve 13760b1

-4	8	-3	5
13760c1	6880e1	123840cr1	68800bf1

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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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