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	3422d	Isogeny class
Conductor	3422	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	312	Modular degree for the optimal curve
Δ	13688 = 23 · 29 · 59	Discriminant
Eigenvalues	2+ -2  2 -2 -5 -3  0  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-15,-22]	[a1,a2,a3,a4,a6]
Generators	[-2:1:1]	Generators of the group modulo torsion
j	338608873/13688	j-invariant
L	1.7807277070801	L(r)(E,1)/r!
Ω	2.4517888802451	Real period
R	0.72629732577224	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	27376i1 109504b1 30798o1 85550y1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3422d1

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
+	-2	2	-2	-5	-3	0	6	9	-	4	-2	0	7	0	-2	-	0	-2	0	-5	9	-10	-6	1

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Quadratic twists for elliptic curve 3422d1

-4	8	-3	5	29
27376i1	109504b1	30798o1	85550y1	99238n1

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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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