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	198c	Isogeny class
Conductor	198	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	32	Modular degree for the optimal curve
Δ	1216512 = 212 · 33 · 11	Discriminant
Eigenvalues	2- 3+  0  2 11+  2 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-65,209]	[a1,a2,a3,a4,a6]
j	1108717875/45056	j-invariant
L	1.8049318292048	L(r)(E,1)/r!
Ω	2.7073977438072	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	1584j1 6336g1 198d3 4950b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 198c1

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 198c1

-4	8	-3	5	-7	-11	13	17	-19	-23
1584j1	6336g1	198d3	4950b1	9702be1	2178a1	33462k1	57222bf1	71478c1	104742bg1

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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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