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	198d	Isogeny class
Conductor	198	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	886837248 = 212 · 39 · 11	Discriminant
Eigenvalues	2+ 3+  0  2 11-  2  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-582,-5068]	[a1,a2,a3,a4,a6]
j	1108717875/45056	j-invariant
L	0.97436372977461	L(r)(E,1)/r!
Ω	0.97436372977461	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	1584h3 6336b3 198c1 4950z3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 198d3

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 198d3

-4	8	-3	5	-7	-11	13	17	-19	-23
1584h3	6336b3	198c1	4950z3	9702i3	2178g3	33462bp3	57222a3	71478bn3	104742a3

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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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