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
deg	15	Modular degree for the optimal curve
Δ	1347921 = 36 · 432	Discriminant
Eigenvalues	1 3-  2  0  0 -2 -6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-30,-29]	[a1,a2,a3,a4,a6]
j	2845178713/1347921	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	2064i2 8256j2 387d2 3225c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 129b1

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 129b1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	-43
2064i2	8256j2	387d2	3225c2	6321a2	15609j2	21801g2	37281b2	46569c2	68241i2	108489a2	123969a2	5547a2

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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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