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	24	Product of Tamagawa factors cp
Δ	209088 = 26 · 33 · 112	Discriminant
Eigenvalues	2- 3+  0  2 11+  2 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1025,12881]	[a1,a2,a3,a4,a6]
j	4406910829875/7744	j-invariant
L	1.8049318292048	L(r)(E,1)/r!
Ω	2.7073977438072	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	1584j2 6336g2 198d4 4950b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 198c2

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 198c2

-4	8	-3	5	-7	-11	13	17	-19	-23
1584j2	6336g2	198d4	4950b2	9702be2	2178a2	33462k2	57222bf2	71478c2	104742bg2

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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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