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	8	Product of Tamagawa factors cp
deg	74880	Modular degree for the optimal curve
Δ	584573027936625 = 32 · 53 · 72 · 139	Discriminant
Eigenvalues	1 3- 5+ 7+  0 13- -4  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-56619,-5057999]	[a1,a2,a3,a4,a6]
Generators	[-761447:449931:4913]	Generators of the group modulo torsion
j	1892819053/55125	j-invariant
L	6.1622541872623	L(r)(E,1)/r!
Ω	0.31005104485549	Real period
R	9.9374833426772	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	53235bi1 88725y1 124215bm1 17745y1	Quadratic twists by: -3 5 -7 13

Hecke Eigenvalues for elliptic curve 17745o1

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 17745o1

-3	5	-7	13
53235bi1	88725y1	124215bm1	17745y1

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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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