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	9744d	Isogeny class
Conductor	9744	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-488291328 = -1 · 210 · 34 · 7 · 292	Discriminant
Eigenvalues	2+ 3-  0 7- -4  0  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,112,-924]	[a1,a2,a3,a4,a6]
Generators	[10:36:1]	Generators of the group modulo torsion
j	150381500/476847	j-invariant
L	5.3207236748117	L(r)(E,1)/r!
Ω	0.8474494918948	Real period
R	0.7848142759097	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	4872a1 38976bk1 29232j1 68208d1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 9744d1

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	-	-4	0	0	0	0	+	10	-10	4	4	-6	-10	-6	10	-16	-8	12	-4	14	4	-8

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Quadratic twists for elliptic curve 9744d1

-4	8	-3	-7
4872a1	38976bk1	29232j1	68208d1

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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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