Cremona's table of elliptic curves

17745 = 3 · 5 · 7 · 13²

Field	Data	Notes
Atkin-Lehner	3- 5+ 7+ 13-	Signs for the Atkin-Lehner involutions
Class	17745o	Isogeny class
Conductor	17745	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	93949236632671875 = 34 · 56 · 7 · 139	Discriminant
Eigenvalues	1 3- 5+ 7+  0 13- -4  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-133514,11612837]	[a1,a2,a3,a4,a6]
Generators	[93:4:1]	Generators of the group modulo torsion
j	24820429213/8859375	j-invariant
L	6.1622541872623	L(r)(E,1)/r!
Ω	0.31005104485549	Real period
R	4.9687416713386	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	53235bi2 88725y2 124215bm2 17745y2	Quadratic twists by: -3 5 -7 13

Hecke Eigenvalues for elliptic curve 17745o2

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
1	-	+	+	0	-	-4	2	-2	2	-2	10	10	6	-8	-6	-10	10	4	-12	6	12	0	6	-2

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Quadratic twists for elliptic curve 17745o2

-3	5	-7	13
53235bi2	88725y2	124215bm2	17745y2

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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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