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	2	Product of Tamagawa factors cp
Δ	48114 = 2 · 37 · 11	Discriminant
Eigenvalues	2+ 3- -2 -4 11- -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-3168,69430]	[a1,a2,a3,a4,a6]
Generators	[33:-14:1]	Generators of the group modulo torsion
j	4824238966273/66	j-invariant
L	0.98827578836306	L(r)(E,1)/r!
Ω	2.5334819295042	Real period
R	0.78017196558925	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	1584n3 6336o3 66b3 4950bl3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 198a3

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 198a3

-4	8	-3	5	-7	-11	13	17	-19	-23
1584n3	6336o3	66b3	4950bl3	9702x3	2178k3	33462ci4	57222h4	71478ct4	104742k4

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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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