Cremona's table of elliptic curves

9744 = 2⁴ · 3 · 7 · 29

Field	Data	Notes
Atkin-Lehner	2- 3- 7+ 29-	Signs for the Atkin-Lehner involutions
Class	9744q	Isogeny class
Conductor	9744	Conductor
∏ cp	96	Product of Tamagawa factors cp
Δ	6810266342455898112 = 212 · 324 · 7 · 292	Discriminant
Eigenvalues	2- 3- -2 7+ -4 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-679504,175033940]	[a1,a2,a3,a4,a6]
j	8471112631466271697/1662662681263647	j-invariant
L	1.3468264955798	L(r)(E,1)/r!
Ω	0.22447108259663	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	609b5 38976bb6 29232ba6 68208bw6	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 9744q5

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	-2	2	4	0	-	8	-10	-6	-12	8	6	-12	-10	12	16	2	0	-4	-6	-6

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Quadratic twists for elliptic curve 9744q5

-4	8	-3	-7
609b5	38976bb6	29232ba6	68208bw6

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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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