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	3422g	Isogeny class
Conductor	3422	Conductor
∏ cp	3	Product of Tamagawa factors cp
deg	8520	Modular degree for the optimal curve
Δ	11911982 = 2 · 29 · 593	Discriminant
Eigenvalues	2-  2 -2 -2 -3  5 -4 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-61939,-5959085]	[a1,a2,a3,a4,a6]
Generators	[-68386422:33956879:474552]	Generators of the group modulo torsion
j	26279477046180740017/11911982	j-invariant
L	5.7578365700437	L(r)(E,1)/r!
Ω	0.30262755619948	Real period
R	6.3420492197879	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	27376d1 109504g1 30798h1 85550e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3422g1

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	-3	5	-4	-6	1	+	0	-10	8	1	-8	-2	-	-8	-6	8	13	15	-14	14	7

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Quadratic twists for elliptic curve 3422g1

-4	8	-3	5	29
27376d1	109504g1	30798h1	85550e1	99238f1

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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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