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	-1729072818 = -1 · 2 · 310 · 114	Discriminant
Eigenvalues	2+ 3- -2 -4 11- -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-108,2074]	[a1,a2,a3,a4,a6]
Generators	[-7:53:1]	Generators of the group modulo torsion
j	-192100033/2371842	j-invariant
L	0.98827578836306	L(r)(E,1)/r!
Ω	1.2667409647521	Real period
R	0.19504299139731	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	1584n4 6336o4 66b4 4950bl4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 198a4

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 198a4

-4	8	-3	5	-7	-11	13	17	-19	-23
1584n4	6336o4	66b4	4950bl4	9702x4	2178k4	33462ci3	57222h3	71478ct3	104742k3

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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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