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	24	Product of Tamagawa factors cp
Δ	191328588 = 22 · 33 · 116	Discriminant
Eigenvalues	2+ 3+  0  2 11-  2  6  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-147,-135]	[a1,a2,a3,a4,a6]
j	13060888875/7086244	j-invariant
L	0.97436372977461	L(r)(E,1)/r!
Ω	1.4615455946619	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	1584h2 6336b2 198c4 4950z2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 198d2

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 198d2

-4	8	-3	5	-7	-11	13	17	-19	-23
1584h2	6336b2	198c4	4950z2	9702i2	2178g2	33462bp2	57222a2	71478bn2	104742a2

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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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