Cremona's table of elliptic curves

3422 = 2 · 29 · 59

Field	Data	Notes
Atkin-Lehner	2- 29+ 59-	Signs for the Atkin-Lehner involutions
Class	3422h	Isogeny class
Conductor	3422	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	2880	Modular degree for the optimal curve
Δ	-1615184 = -1 · 24 · 29 · 592	Discriminant
Eigenvalues	2- -3  3 -2 -3 -5  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-786,8673]	[a1,a2,a3,a4,a6]
Generators	[7:55:1]	Generators of the group modulo torsion
j	-53638082426097/1615184	j-invariant
L	3.5353324909559	L(r)(E,1)/r!
Ω	2.4854943905022	Real period
R	0.17779825336085	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	27376e1 109504i1 30798j1 85550f1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3422h1

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

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Quadratic twists for elliptic curve 3422h1

-4	8	-3	5	29
27376e1	109504i1	30798j1	85550f1	99238g1

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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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