Cremona's table of elliptic curves

6171 = 3 · 11² · 17

Field	Data	Notes
Atkin-Lehner	3- 11+ 17-	Signs for the Atkin-Lehner involutions
Class	6171c	Isogeny class
Conductor	6171	Conductor
∏ cp	20	Product of Tamagawa factors cp
Δ	1336101723 = 310 · 113 · 17	Discriminant
Eigenvalues	-1 3-  0  2 11+  0 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1053,-13122]	[a1,a2,a3,a4,a6]
Generators	[-18:18:1]	Generators of the group modulo torsion
j	97018944875/1003833	j-invariant
L	3.2766790885756	L(r)(E,1)/r!
Ω	0.83861323084617	Real period
R	0.78145179876769	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	98736bp2 18513h2 6171b2 104907b2	Quadratic twists by: -4 -3 -11 17

Hecke Eigenvalues for elliptic curve 6171c2

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	-	0	2	+	0	-	-4	4	2	-8	6	-6	-12	2	-10	-14	10	8	12	-6	-10	-12	6	-6

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Quadratic twists for elliptic curve 6171c2

-4	-3	-11	17
98736bp2	18513h2	6171b2	104907b2

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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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