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	8	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	384912 = 24 · 37 · 11	Discriminant
Eigenvalues	2+ 3- -2 -4 11- -6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-18,4]	[a1,a2,a3,a4,a6]
Generators	[-1:5:1]	Generators of the group modulo torsion
j	912673/528	j-invariant
L	0.98827578836306	L(r)(E,1)/r!
Ω	2.5334819295042	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	1584n1 6336o1 66b1 4950bl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 198a1

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 198a1

-4	8	-3	5	-7	-11	13	17	-19	-23
1584n1	6336o1	66b1	4950bl1	9702x1	2178k1	33462ci1	57222h1	71478ct1	104742k1

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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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