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	8398a	Isogeny class
Conductor	8398	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2944	Modular degree for the optimal curve
Δ	-18274048 = -1 · 28 · 13 · 172 · 19	Discriminant
Eigenvalues	2+ -2  0 -2 -6 13+ 17+ 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-86,360]	[a1,a2,a3,a4,a6]
Generators	[5:5:1]	Generators of the group modulo torsion
j	-69173457625/18274048	j-invariant
L	1.4354700372334	L(r)(E,1)/r!
Ω	2.0724330922042	Real period
R	0.69264964096219	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	67184n1 75582bd1 109174j1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 8398a1

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	+	+	+	-4	4	8	-10	10	4	12	2	-4	6	12	12	-8	10	4	-14	-2

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Quadratic twists for elliptic curve 8398a1

-4	-3	13
67184n1	75582bd1	109174j1

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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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