Cremona's table of elliptic curves

129 = 3 · 43

Field	Data	Notes
Atkin-Lehner	3- 43+	Signs for the Atkin-Lehner involutions
Class	129b	Isogeny class
Conductor	129	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	22851963 = 312 · 43	Discriminant
Eigenvalues	1 3-  2  0  0 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-245,1433]	[a1,a2,a3,a4,a6]
j	1616855892553/22851963	j-invariant
L	1.6091464597883	L(r)(E,1)/r!
Ω	2.145528613051	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2064i3 8256j3 387d3 3225c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 129b3

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

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Quadratic twists for elliptic curve 129b3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	-43
2064i3	8256j3	387d3	3225c3	6321a3	15609j3	21801g4	37281b4	46569c4	68241i4	108489a4	123969a4	5547a3

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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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