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	9744h	Isogeny class
Conductor	9744	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-564135485964288 = -1 · 216 · 3 · 76 · 293	Discriminant
Eigenvalues	2- 3+  0 7+  0  2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,17072,748480]	[a1,a2,a3,a4,a6]
j	134335727363375/137728390128	j-invariant
L	0.68403608144298	L(r)(E,1)/r!
Ω	0.34201804072149	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1218k3 38976bq3 29232bc3 68208cf3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 9744h3

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

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Quadratic twists for elliptic curve 9744h3

-4	8	-3	-7
1218k3	38976bq3	29232bc3	68208cf3

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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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