Cremona's table of elliptic curves

7744 = 2⁶ · 11²

Field	Data	Notes
Atkin-Lehner	2- 11-	Signs for the Atkin-Lehner involutions
Class	7744z	Isogeny class
Conductor	7744	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3840	Modular degree for the optimal curve
Δ	-1247178944 = -1 · 26 · 117	Discriminant
Eigenvalues	2- -1 -1 -4 11- -2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1371,20077]	[a1,a2,a3,a4,a6]
Generators	[4:121:1]	Generators of the group modulo torsion
j	-2515456/11	j-invariant
L	2.4147112523879	L(r)(E,1)/r!
Ω	1.5408205599574	Real period
R	0.39178982211508	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	7744w1 3872i1 69696fy1 704g1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 7744z1

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
-	-1	-1	-4	-	-2	0	-2	9	4	5	9	-2	-6	-4	6	5	0	13	-1	-14	10	14	-13	-19

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Quadratic twists for elliptic curve 7744z1

-4	8	-3	-11
7744w1	3872i1	69696fy1	704g1

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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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