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	1760f	Isogeny class
Conductor	1760	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	128	Modular degree for the optimal curve
Δ	193600 = 26 · 52 · 112	Discriminant
Eigenvalues	2+  0 5-  0 11- -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-37,84]	[a1,a2,a3,a4,a6]
Generators	[-5:12:1]	Generators of the group modulo torsion
j	87528384/3025	j-invariant
L	2.9697458586054	L(r)(E,1)/r!
Ω	3.163487560955	Real period
R	1.8775138522808	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1760j1 3520a2 15840s1 8800u1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1760f1

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
+	0	-	0	-	-2	-2	-4	0	-6	4	-10	-6	4	-8	6	12	2	8	-12	-2	-8	-12	-6	-6

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Quadratic twists for elliptic curve 1760f1

-4	8	-3	5	-7	-11
1760j1	3520a2	15840s1	8800u1	86240f1	19360v1

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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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