Cremona's table of elliptic curves

171 = 3² · 19

Field	Data	Notes
Atkin-Lehner	3- 19+	Signs for the Atkin-Lehner involutions
Class	171d	Isogeny class
Conductor	171	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	-124659 = -1 · 38 · 19	Discriminant
Eigenvalues	2 3-  3 -5 -1  2  1 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-21,-41]	[a1,a2,a3,a4,a6]
j	-1404928/171	j-invariant
L	2.2150961108224	L(r)(E,1)/r!
Ω	1.1075480554112	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2736w1 10944bk1 57a1 4275j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 171d1

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
2	-	3	-5	-1	2	1	+	4	2	-6	0	0	-1	9	-10	8	-1	8	12	-11	16	-12	6	-10

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Quadratic twists for elliptic curve 171d1

-4	8	-3	5	-7	-11	13	17	-19	-23
2736w1	10944bk1	57a1	4275j1	8379p1	20691s1	28899s1	49419d1	3249g1	90459t1

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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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