Cremona's table of elliptic curves

42891 = 3 · 17 · 29²

Field	Data	Notes
Atkin-Lehner	3- 17+ 29+	Signs for the Atkin-Lehner involutions
Class	42891i	Isogeny class
Conductor	42891	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	11040	Modular degree for the optimal curve
Δ	-210723483 = -1 · 3 · 174 · 292	Discriminant
Eigenvalues	0 3-  0 -1  6 -2 17+ -3	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-193,-1313]	[a1,a2,a3,a4,a6]
j	-950272000/250563	j-invariant
L	1.262920308036	L(r)(E,1)/r!
Ω	0.63146015393946	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	128673k1 42891h1	Quadratic twists by: -3 29

Hecke Eigenvalues for elliptic curve 42891i1

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	-	0	-1	6	-2	+	-3	-4	+	-8	-3	2	-1	-2	-2	6	-3	-13	-6	14	-7	-12	-4	-10

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Quadratic twists for elliptic curve 42891i1

-3	29
128673k1	42891h1

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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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