Cremona's table of elliptic curves

6422 = 2 · 13² · 19

Field	Data	Notes
Atkin-Lehner	2- 13- 19+	Signs for the Atkin-Lehner involutions
Class	6422j	Isogeny class
Conductor	6422	Conductor
∏ cp	140	Product of Tamagawa factors cp
deg	43680	Modular degree for the optimal curve
Δ	-27251292615213056 = -1 · 235 · 133 · 192	Discriminant
Eigenvalues	2-  1 -3  1  2 13-  1 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-17092,-7990256]	[a1,a2,a3,a4,a6]
Generators	[264:2300:1]	Generators of the group modulo torsion
j	-251347109804029/12403865550848	j-invariant
L	5.9890857407624	L(r)(E,1)/r!
Ω	0.16436184254478	Real period
R	0.2602744237972	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	51376bc1 57798y1 6422d1 122018s1	Quadratic twists by: -4 -3 13 -19

Hecke Eigenvalues for elliptic curve 6422j1

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	-3	1	2	-	1	+	-4	2	-4	3	10	-11	-3	0	-6	6	-2	-3	-4	-6	-14	8	16

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Quadratic twists for elliptic curve 6422j1

-4	-3	13	-19
51376bc1	57798y1	6422d1	122018s1

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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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