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	17745q	Isogeny class
Conductor	17745	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	32256	Modular degree for the optimal curve
Δ	32942971425 = 3 · 52 · 7 · 137	Discriminant
Eigenvalues	-1 3- 5+ 7- -4 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-24086,-1440765]	[a1,a2,a3,a4,a6]
Generators	[611385:996368:3375]	Generators of the group modulo torsion
j	320153881321/6825	j-invariant
L	3.2393110854344	L(r)(E,1)/r!
Ω	0.38322942342612	Real period
R	8.4526680036062	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	53235bj1 88725e1 124215bf1 1365f1	Quadratic twists by: -3 5 -7 13

Hecke Eigenvalues for elliptic curve 17745q1

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	-	+	-	-4	+	-2	-4	4	6	-8	2	-2	-4	12	-2	0	14	4	0	-10	-8	0	6	14

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Quadratic twists for elliptic curve 17745q1

-3	5	-7	13
53235bj1	88725e1	124215bf1	1365f1

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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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