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	8	Product of Tamagawa factors cp
Δ	152425152 = 26 · 39 · 112	Discriminant
Eigenvalues	2+ 3+  0  2 11-  2  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-9222,-338572]	[a1,a2,a3,a4,a6]
j	4406910829875/7744	j-invariant
L	0.97436372977461	L(r)(E,1)/r!
Ω	0.48718186488731	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	1584h4 6336b4 198c2 4950z4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 198d4

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 198d4

-4	8	-3	5	-7	-11	13	17	-19	-23
1584h4	6336b4	198c2	4950z4	9702i4	2178g4	33462bp4	57222a4	71478bn4	104742a4

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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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