Cremona's table of elliptic curves

493 = 17 · 29

Field	Data	Notes
Atkin-Lehner	17- 29-	Signs for the Atkin-Lehner involutions
Class	493b	Isogeny class
Conductor	493	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	120	Modular degree for the optimal curve
Δ	-7048421 = -1 · 172 · 293	Discriminant
Eigenvalues	-1 -3  1 -2  3  1 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-57,222]	[a1,a2,a3,a4,a6]
Generators	[40:226:1]	Generators of the group modulo torsion
j	-20145851361/7048421	j-invariant
L	0.90924727333784	L(r)(E,1)/r!
Ω	2.2243974246595	Real period
R	0.068126860129848	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	7888j1 31552i1 4437e1 12325d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 493b1

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	-3	1	-2	3	1	-	-4	-2	-	1	-2	6	1	-9	-9	-6	8	-14	-10	0	3	8	16	2

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Quadratic twists for elliptic curve 493b1

-4	8	-3	5	-7	-11	13	17	29
7888j1	31552i1	4437e1	12325d1	24157e1	59653a1	83317i1	8381b1	14297c1

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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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