Cremona's table of elliptic curves

171 = 3² · 19

Field	Data	Notes
Atkin-Lehner	3- 19+	Signs for the Atkin-Lehner involutions
Class	171c	Isogeny class
Conductor	171	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	-817887699 = -1 · 316 · 19	Discriminant
Eigenvalues	2 3- -1  3  3 -6 -3 19+	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,177,1035]	[a1,a2,a3,a4,a6]
j	841232384/1121931	j-invariant
L	2.1401740379046	L(r)(E,1)/r!
Ω	1.0700870189523	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	2736s1 10944z1 57c1 4275i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 171c1

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	-	-1	3	3	-6	-3	+	-4	10	2	8	8	-1	-3	6	0	7	8	-12	-11	0	-4	-10	-2

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Quadratic twists for elliptic curve 171c1

-4	8	-3	5	-7	-11	13	17	-19	-23
2736s1	10944z1	57c1	4275i1	8379o1	20691r1	28899r1	49419c1	3249f1	90459s1

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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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