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	198a	Isogeny class
Conductor	198	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	3175524 = 22 · 38 · 112	Discriminant
Eigenvalues	2+ 3- -2 -4 11- -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-198,1120]	[a1,a2,a3,a4,a6]
Generators	[2:26:1]	Generators of the group modulo torsion
j	1180932193/4356	j-invariant
L	0.98827578836306	L(r)(E,1)/r!
Ω	2.5334819295042	Real period
R	0.39008598279462	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1584n2 6336o2 66b2 4950bl2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 198a2

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

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Quadratic twists for elliptic curve 198a2

-4	8	-3	5	-7	-11	13	17	-19	-23
1584n2	6336o2	66b2	4950bl2	9702x2	2178k2	33462ci2	57222h2	71478ct2	104742k2

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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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