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	8398g	Isogeny class
Conductor	8398	Conductor
∏ cp	72	Product of Tamagawa factors cp
Δ	9457094658411062 = 2 · 134 · 176 · 193	Discriminant
Eigenvalues	2+ -2  0  2  0 13- 17- 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-90461,9361290]	[a1,a2,a3,a4,a6]
j	81865508515272807625/9457094658411062	j-invariant
L	0.79219233827849	L(r)(E,1)/r!
Ω	0.39609616913925	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	67184u2 75582bn2 109174m2	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 8398g2

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	0	-	-	-	-6	6	-4	2	0	-4	0	6	0	8	-4	0	14	-4	12	-6	-16

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Quadratic twists for elliptic curve 8398g2

-4	-3	13
67184u2	75582bn2	109174m2

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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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