Cremona's table of elliptic curves

7744 = 2⁶ · 11²

Field	Data	Notes
Atkin-Lehner	2- 11-	Signs for the Atkin-Lehner involutions
Class	7744t	Isogeny class
Conductor	7744	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	58050510848 = 215 · 116	Discriminant
Eigenvalues	2-  0  2  0 11-  6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-5324,149072]	[a1,a2,a3,a4,a6]
Generators	[26:168:1]	Generators of the group modulo torsion
j	287496	j-invariant
L	4.7552248969626	L(r)(E,1)/r!
Ω	1.1180490978014	Real period
R	2.1265724851947	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	7744t3 3872b3 69696gm3 64a2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 7744t4

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	0	-	6	-2	0	0	-10	0	2	-10	0	0	-14	0	-10	0	0	6	0	0	10	18

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Quadratic twists for elliptic curve 7744t4

-4	8	-3	-11
7744t3	3872b3	69696gm3	64a2

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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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