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	8	Product of Tamagawa factors cp
Δ	2368521 = 38 · 192	Discriminant
Eigenvalues	-1 3-  2  0  0  6  6 19+	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-59,-142]	[a1,a2,a3,a4,a6]
j	30664297/3249	j-invariant
L	0.86836134047839	L(r)(E,1)/r!
Ω	1.7367226809568	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2736t2 10944bh2 57b1 4275e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 171a2

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 171a2

-4	8	-3	5	-7	-11	13	17	-19	-23
2736t2	10944bh2	57b1	4275e2	8379n2	20691q2	28899k2	49419b2	3249e2	90459r2

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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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