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	198b	Isogeny class
Conductor	198	Conductor
∏ cp	72	Product of Tamagawa factors cp
Δ	-92985693768 = -1 · 23 · 38 · 116	Discriminant
Eigenvalues	2- 3-  0  2 11- -4  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-365,15005]	[a1,a2,a3,a4,a6]
j	-7357983625/127552392	j-invariant
L	1.8053975905613	L(r)(E,1)/r!
Ω	0.90269879528067	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	1584l4 6336k4 66a4 4950o4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 198b4

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	-	-4	6	-4	-6	-6	8	-10	-6	8	6	0	0	8	-4	-6	2	14	12	6	14

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Quadratic twists for elliptic curve 198b4

-4	8	-3	5	-7	-11	13	17	-19	-23
1584l4	6336k4	66a4	4950o4	9702ca4	2178c4	33462q4	57222bh4	71478ba4	104742bl4

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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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