Cremona's table of elliptic curves

171 = 3² · 19

Field	Data	Notes
Atkin-Lehner	3- 19+	Signs for the Atkin-Lehner involutions
Class	171a	Isogeny class
Conductor	171	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	1121931 = 310 · 19	Discriminant
Eigenvalues	-1 3-  2  0  0  6  6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-914,-10402]	[a1,a2,a3,a4,a6]
j	115714886617/1539	j-invariant
L	0.86836134047839	L(r)(E,1)/r!
Ω	0.86836134047839	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2736t3 10944bh3 57b3 4275e3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 171a3

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	-	2	0	0	6	6	+	-4	-2	8	-10	2	-4	-12	6	12	-2	-4	0	10	0	-16	2	10

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Quadratic twists for elliptic curve 171a3

-4	8	-3	5	-7	-11	13	17	-19	-23
2736t3	10944bh3	57b3	4275e3	8379n3	20691q3	28899k4	49419b4	3249e3	90459r4

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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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