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	3422a	Isogeny class
Conductor	3422	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1728	Modular degree for the optimal curve
Δ	-22489822016 = -1 · 26 · 29 · 594	Discriminant
Eigenvalues	2+  1  1 -2 -1  3  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-253,-7400]	[a1,a2,a3,a4,a6]
Generators	[1785:13018:27]	Generators of the group modulo torsion
j	-1780800847561/22489822016	j-invariant
L	3.000500345307	L(r)(E,1)/r!
Ω	0.5141536958743	Real period
R	1.4589510730857	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	27376f1 109504k1 30798t1 85550p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3422a1

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	1	-2	-1	3	0	0	0	+	7	-8	6	7	-9	5	+	0	-8	-6	-8	-15	4	6	-14

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Quadratic twists for elliptic curve 3422a1

-4	8	-3	5	29
27376f1	109504k1	30798t1	85550p1	99238k1

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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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