Cremona's table of elliptic curves

9198 = 2 · 3² · 7 · 73

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 73-	Signs for the Atkin-Lehner involutions
Class	9198d	Isogeny class
Conductor	9198	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	1590600472681248 = 25 · 36 · 74 · 734	Discriminant
Eigenvalues	2+ 3-  2 7+  0 -2 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-50496,-3910816]	[a1,a2,a3,a4,a6]
Generators	[275:1578:1]	Generators of the group modulo torsion
j	19533135070647297/2181893652512	j-invariant
L	3.5639565188619	L(r)(E,1)/r!
Ω	0.32079419103601	Real period
R	2.7774478298313	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	73584bh3 1022b3 64386r3	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 9198d4

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	+	0	-2	-2	0	8	6	0	-10	-2	-8	-8	-2	-4	2	4	0	-	8	4	6	10

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Quadratic twists for elliptic curve 9198d4

-4	-3	-7
73584bh3	1022b3	64386r3

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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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