Cremona's table of elliptic curves

198 = 2 · 3² · 11

Field	Data	Notes
Atkin-Lehner	2- 3+ 11+	Signs for the Atkin-Lehner involutions
Class	198c	Isogeny class
Conductor	198	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	419169168 = 24 · 39 · 113	Discriminant
Eigenvalues	2- 3+  0  2 11+  2 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-785,-8207]	[a1,a2,a3,a4,a6]
j	2714704875/21296	j-invariant
L	1.8049318292048	L(r)(E,1)/r!
Ω	0.90246591460241	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	1584j3 6336g3 198d1 4950b3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 198c3

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
-	+	0	2	+	2	-6	2	0	-6	-4	2	6	-10	12	-12	12	-10	8	12	14	2	-12	0	2

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Quadratic twists for elliptic curve 198c3

-4	8	-3	5	-7	-11	13	17	-19	-23
1584j3	6336g3	198d1	4950b3	9702be3	2178a3	33462k3	57222bf3	71478c3	104742bg3

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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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