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	1760b	Isogeny class
Conductor	1760	Conductor
∏ cp	4	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	[-10:6:1]	Generators of the group modulo torsion
j	3484156096/1830125	j-invariant
L	3.4897204639137	L(r)(E,1)/r!
Ω	1.5098523228593	Real period
R	2.311299198656	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	1760i1 3520n2 15840bg1 8800s1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1760b1

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 1760b1

-4	8	-3	5	-7	-11
1760i1	3520n2	15840bg1	8800s1	86240m1	19360t1

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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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