Cremona's table of elliptic curves

129 = 3 · 43

Field	Data	Notes
Atkin-Lehner	3+ 43+	Signs for the Atkin-Lehner involutions
Class	129a	Isogeny class
Conductor	129	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-3483 = -1 · 34 · 43	Discriminant
Eigenvalues	0 3+ -2 -2 -5  3 -3  2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-19,39]	[a1,a2,a3,a4,a6]
Generators	[1:4:1]	Generators of the group modulo torsion
j	-799178752/3483	j-invariant
L	0.89419550928556	L(r)(E,1)/r!
Ω	4.4728045672092	Real period
R	0.099959152680293	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	2064m1 8256v1 387a1 3225f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 129a1

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
0	+	-2	-2	-5	3	-3	2	-1	0	-5	8	-7	+	-8	3	12	-8	-15	-14	12	-16	15	10	11

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Quadratic twists for elliptic curve 129a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	-43
2064m1	8256v1	387a1	3225f1	6321e1	15609f1	21801a1	37281c1	46569h1	68241b1	108489j1	123969c1	5547d1

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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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