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	6422a	Isogeny class
Conductor	6422	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	52416	Modular degree for the optimal curve
Δ	-31360813249765376 = -1 · 213 · 139 · 192	Discriminant
Eigenvalues	2+ -1  1  3  4 13+ -3 19-	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-169172,28034128]	[a1,a2,a3,a4,a6]
j	-110931033861649/6497214464	j-invariant
L	1.4618026318462	L(r)(E,1)/r!
Ω	0.36545065796154	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	51376m1 57798bl1 494d1 122018be1	Quadratic twists by: -4 -3 13 -19

Hecke Eigenvalues for elliptic curve 6422a1

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	3	4	+	-3	-	2	4	8	-1	-10	-5	7	2	6	2	0	-5	0	8	12	0	2

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Quadratic twists for elliptic curve 6422a1

-4	-3	13	-19
51376m1	57798bl1	494d1	122018be1

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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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