Cremona's table of elliptic curves

1760 = 2⁵ · 5 · 11

Field	Data	Notes
Atkin-Lehner	2- 5+ 11-	Signs for the Atkin-Lehner involutions
Class	1760i	Isogeny class
Conductor	1760	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	117128000 = 26 · 53 · 114	Discriminant
Eigenvalues	2- -2 5+  2 11- -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-126,124]	[a1,a2,a3,a4,a6]
Generators	[-10:22:1]	Generators of the group modulo torsion
j	3484156096/1830125	j-invariant
L	2.1043520385562	L(r)(E,1)/r!
Ω	1.6396207243987	Real period
R	0.64171915103352	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1760b1 3520k2 15840q1 8800g1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1760i1

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	-	-2	-2	0	2	-2	4	-6	6	-6	6	-6	0	-6	2	4	-10	-8	-14	10	-14

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Quadratic twists for elliptic curve 1760i1

-4	8	-3	5	-7	-11
1760b1	3520k2	15840q1	8800g1	86240bz1	19360f1

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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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