Cremona's table of elliptic curves

171 = 3² · 19

Field	Data	Notes
Atkin-Lehner	3- 19-	Signs for the Atkin-Lehner involutions
Class	171b	Isogeny class
Conductor	171	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	-5000211 = -1 · 36 · 193	Discriminant
Eigenvalues	0 3- -3 -1 -3 -4  3 19-	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-84,315]	[a1,a2,a3,a4,a6]
Generators	[5:4:1]	Generators of the group modulo torsion
j	-89915392/6859	j-invariant
L	1.0768577238443	L(r)(E,1)/r!
Ω	2.3827779033284	Real period
R	0.67790060647708	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	2736q2 10944t2 19a1 4275k2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 171b2

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 elliptic curve 171b2

-4	8	-3	5	-7	-11	13	17	-19	-23
2736q2	10944t2	19a1	4275k2	8379f2	20691o2	28899c2	49419f2	3249c2	90459l2

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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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