Cremona's table of elliptic curves

8398 = 2 · 13 · 17 · 19

Field	Data	Notes
Atkin-Lehner	2- 13- 17+ 19-	Signs for the Atkin-Lehner involutions
Class	8398i	Isogeny class
Conductor	8398	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	156248215426628 = 22 · 132 · 173 · 196	Discriminant
Eigenvalues	2- -2  0  2 -6 13- 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-102953,-12709067]	[a1,a2,a3,a4,a6]
j	120681581978584068625/156248215426628	j-invariant
L	1.599281069027	L(r)(E,1)/r!
Ω	0.26654684483783	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	67184s4 75582q4 109174b4	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 8398i4

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	0	2	-6	-	+	-	0	0	-4	2	6	-4	0	6	12	-10	-4	0	-4	14	12	6	2

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Quadratic twists for elliptic curve 8398i4

-4	-3	13
67184s4	75582q4	109174b4

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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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