Cremona's table of elliptic curves

7744 = 2⁶ · 11²

Field	Data	Notes
Atkin-Lehner	2- 11-	Signs for the Atkin-Lehner involutions
Class	7744u	Isogeny class
Conductor	7744	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-7929856 = -1 · 216 · 112	Discriminant
Eigenvalues	2-  0 -3  4 11-  3 -3 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-44,-176]	[a1,a2,a3,a4,a6]
Generators	[12:32:1]	Generators of the group modulo torsion
j	-1188	j-invariant
L	3.749201786271	L(r)(E,1)/r!
Ω	0.89501393370202	Real period
R	2.0944935297059	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	7744e1 1936c1 69696gt1 7744v1	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 7744u1

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	-3	4	-	3	-3	-4	8	-5	4	-11	-7	12	8	1	-4	-2	4	-12	-10	8	-4	3	-13

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Quadratic twists for elliptic curve 7744u1

-4	8	-3	-11
7744e1	1936c1	69696gt1	7744v1

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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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