Cremona's table of elliptic curves

171 = 3² · 19

Field	Data	Notes
Atkin-Lehner	3- 19-	Signs for the Atkin-Lehner involutions
Class	171b	Isogeny class
Conductor	171	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-13851 = -1 · 36 · 19	Discriminant
Eigenvalues	0 3- -3 -1 -3 -4  3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-6924,221760]	[a1,a2,a3,a4,a6]
Generators	[62:175:1]	Generators of the group modulo torsion
j	-50357871050752/19	j-invariant
L	1.0768577238443	L(r)(E,1)/r!
Ω	2.3827779033284	Real period
R	2.0337018194313	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	2736q3 10944t3 19a2 4275k3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 171b3

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	-	-3	-1	-3	-4	3	-	0	-6	-4	2	6	-1	3	-12	6	-1	-4	-6	-7	8	-12	-12	8

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Quadratic twists for elliptic curve 171b3

-4	8	-3	5	-7	-11	13	17	-19	-23
2736q3	10944t3	19a2	4275k3	8379f3	20691o3	28899c3	49419f3	3249c3	90459l3

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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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