Cremona's table of elliptic curves

171 = 3² · 19

Field	Data	Notes
Atkin-Lehner	3- 19-	Signs for the Atkin-Lehner involutions
Conductor	171	Conductor
Count	3	Number of curves in isogeny class
Curves	171b1 171b2 171b3	Curves in isogeny class
deg	8	Modular degree for the optimal curve
Eigenvalues	0 3- -3 -1 -3 -4  3 19-	Hecke eigenvalues for primes less than 20
L	1.0768577238443	L(r)(E,1)/r!
r	1	Rank of the group of rational points
Twists	2736q 10944t 19a 4275k	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for isogeny class 171b

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 isogeny class 171b

-4	8	-3	5	-7	-11	13	17	-19	-23
2736q	10944t	19a	4275k	8379f	20691o	28899c	49419f	3249c	90459l

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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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