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	4	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	866052 = 22 · 39 · 11	Discriminant
Eigenvalues	2- 3-  0  2 11- -4  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-50,-115]	[a1,a2,a3,a4,a6]
j	18609625/1188	j-invariant
L	1.8053975905613	L(r)(E,1)/r!
Ω	1.8053975905613	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	1584l1 6336k1 66a1 4950o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 198b1

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 198b1

-4	8	-3	5	-7	-11	13	17	-19	-23
1584l1	6336k1	66a1	4950o1	9702ca1	2178c1	33462q1	57222bh1	71478ba1	104742bl1

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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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