Cremona's table of elliptic curves

3179 = 11 · 17²

Field	Data	Notes
Atkin-Lehner	11+ 17+	Signs for the Atkin-Lehner involutions
Class	3179b	Isogeny class
Conductor	3179	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	324	Modular degree for the optimal curve
Δ	-384659 = -1 · 113 · 172	Discriminant
Eigenvalues	2  0 -1  2 11+ -2 17+  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,17,-13]	[a1,a2,a3,a4,a6]
Generators	[50:143:8]	Generators of the group modulo torsion
j	1880064/1331	j-invariant
L	6.0291721462912	L(r)(E,1)/r!
Ω	1.6948415592055	Real period
R	3.5573662408406	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	50864bm1 28611x1 79475f1 34969i1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3179b1

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	0	-1	2	+	-2	+	2	-1	0	5	-10	6	-8	-3	-6	-12	-2	-11	-5	12	0	8	7	-5

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Quadratic twists for elliptic curve 3179b1

-4	-3	5	-11	17
50864bm1	28611x1	79475f1	34969i1	3179g1

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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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