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	1125023219712 = 218 · 36 · 7 · 292	Discriminant
Eigenvalues	2- 3+  0 7+  0  2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-37968,-2834496]	[a1,a2,a3,a4,a6]
j	1477843225692625/274663872	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	1218k2 38976bq2 29232bc2 68208cf2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 9744h2

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 9744h2

-4	8	-3	-7
1218k2	38976bq2	29232bc2	68208cf2

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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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