Cremona's table of elliptic curves

3179 = 11 · 17²

Field	Data	Notes
Atkin-Lehner	11+ 17+	Signs for the Atkin-Lehner involutions
Class	3179c	Isogeny class
Conductor	3179	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-3887379625019 = -1 · 115 · 176	Discriminant
Eigenvalues	-2  1 -1  2 11+  4 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-2986,-114768]	[a1,a2,a3,a4,a6]
Generators	[666:3753:8]	Generators of the group modulo torsion
j	-122023936/161051	j-invariant
L	2.0565038376413	L(r)(E,1)/r!
Ω	0.30782847191537	Real period
R	3.3403405228329	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	50864bo2 28611w2 79475e2 34969h2	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3179c2

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	-1	2	+	4	+	0	1	0	-7	-3	8	-6	8	-6	5	-12	-7	3	-4	10	-6	15	7

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Quadratic twists for elliptic curve 3179c2

-4	-3	5	-11	17
50864bo2	28611w2	79475e2	34969h2	11a1

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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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