Cremona's table of elliptic curves

329 = 7 · 47

Field	Data	Notes
Atkin-Lehner	7+ 47-	Signs for the Atkin-Lehner involutions
Class	329a	Isogeny class
Conductor	329	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	180	Modular degree for the optimal curve
Δ	-1896619529 = -1 · 79 · 47	Discriminant
Eigenvalues	-1 -1  3 7+  3 -6  6  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,246,-1376]	[a1,a2,a3,a4,a6]
j	1645957774943/1896619529	j-invariant
L	0.79689202644526	L(r)(E,1)/r!
Ω	0.79689202644526	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	5264j1 21056g1 2961e1 8225b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 329a1

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	-1	3	+	3	-6	6	8	4	2	6	9	-5	-9	-	-1	3	-4	4	0	-13	8	7	-4	-6

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Quadratic twists for elliptic curve 329a1

-4	8	-3	5	-7	-11	13	17	-19	-47
5264j1	21056g1	2961e1	8225b1	2303a1	39809a1	55601d1	95081d1	118769a1	15463a1

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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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