Cremona's table of elliptic curves

17160 = 2³ · 3 · 5 · 11 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 11+ 13+	Signs for the Atkin-Lehner involutions
Class	17160j	Isogeny class
Conductor	17160	Conductor
∏ cp	128	Product of Tamagawa factors cp
deg	645120	Modular degree for the optimal curve
Δ	-3.3917681536744E+20	Discriminant
Eigenvalues	2+ 3- 5-  0 11+ 13+  7 -5	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,825575,837992363]	[a1,a2,a3,a4,a6]
Generators	[-373:21870:1]	Generators of the group modulo torsion
j	243082010896493302784/1324909435029066315	j-invariant
L	6.5732932215725	L(r)(E,1)/r!
Ω	0.12325630342765	Real period
R	0.41664281554315	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	34320i1 51480bo1 85800bt1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 17160j1

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	+	+	7	-5	2	4	-2	-7	-9	-11	-3	0	2	-14	-7	14	-4	6	10	-14	-13

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Quadratic twists for elliptic curve 17160j1

-4	-3	5
34320i1	51480bo1	85800bt1

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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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