Cremona's table of elliptic curves

6474 = 2 · 3 · 13 · 83

Field	Data	Notes
Atkin-Lehner	2- 3- 13- 83-	Signs for the Atkin-Lehner involutions
Class	6474k	Isogeny class
Conductor	6474	Conductor
∏ cp	196	Product of Tamagawa factors cp
deg	9408	Modular degree for the optimal curve
Δ	-502612770816 = -1 · 214 · 37 · 132 · 83	Discriminant
Eigenvalues	2- 3- -3 -2 -3 13-  2  5	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,1703,20921]	[a1,a2,a3,a4,a6]
Generators	[2:155:1]	Generators of the group modulo torsion
j	546200027079407/502612770816	j-invariant
L	5.6432812642806	L(r)(E,1)/r!
Ω	0.60806103222218	Real period
R	0.047350923382063	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	51792j1 19422g1 84162e1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 6474k1

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
-	-	-3	-2	-3	-	2	5	5	6	-4	-9	-6	-8	-4	-5	-5	5	7	-6	-4	-8	-	-3	2

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Quadratic twists for elliptic curve 6474k1

-4	-3	13
51792j1	19422g1	84162e1

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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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