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	9744n	Isogeny class
Conductor	9744	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	13824	Modular degree for the optimal curve
Δ	-42535600128 = -1 · 214 · 32 · 73 · 292	Discriminant
Eigenvalues	2- 3+ -4 7- -4  0  0 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,720,6336]	[a1,a2,a3,a4,a6]
Generators	[-6:42:1] [8:112:1]	Generators of the group modulo torsion
j	10063705679/10384668	j-invariant
L	4.398377925926	L(r)(E,1)/r!
Ω	0.75481852966849	Real period
R	0.48558889245623	Regulator
r	2	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1218j1 38976bz1 29232bs1 68208dc1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 9744n1

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
-	+	-4	-	-4	0	0	-8	-8	-	2	-6	-4	-12	-2	-14	6	6	0	8	8	-16	-6	-12	-12

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Quadratic twists for elliptic curve 9744n1

-4	8	-3	-7
1218j1	38976bz1	29232bs1	68208dc1

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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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