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	9744t	Isogeny class
Conductor	9744	Conductor
∏ cp	120	Product of Tamagawa factors cp
Δ	2218450206244608 = 28 · 36 · 75 · 294	Discriminant
Eigenvalues	2- 3-  0 7- -2  2 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-82068,-8788248]	[a1,a2,a3,a4,a6]
Generators	[903:25578:1]	Generators of the group modulo torsion
j	238786949809042000/8665821118143	j-invariant
L	5.4947424223812	L(r)(E,1)/r!
Ω	0.28269870351484	Real period
R	0.64789147763611	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	2436a2 38976be2 29232bj2 68208bp2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 9744t2

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	-	-2	2	-4	4	2	-	-8	-6	0	0	-12	-6	0	-6	-8	14	-6	16	-12	-8	10

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Quadratic twists for elliptic curve 9744t2

-4	8	-3	-7
2436a2	38976be2	29232bj2	68208bp2

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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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