Cremona's table of elliptic curves

7744 = 2⁶ · 11²

Field	Data	Notes
Atkin-Lehner	2+ 11-	Signs for the Atkin-Lehner involutions
Class	7744h	Isogeny class
Conductor	7744	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-38632614969344 = -1 · 214 · 119	Discriminant
Eigenvalues	2+ -1  3 -2 11- -4 -6  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-37429,2815661]	[a1,a2,a3,a4,a6]
j	-199794688/1331	j-invariant
L	1.302259704607	L(r)(E,1)/r!
Ω	0.65112985230351	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	7744x2 484a2 69696di2 704d2	Quadratic twists by: -4 8 -3 -11

Hecke Eigenvalues for elliptic curve 7744h2

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	3	-2	-	-4	-6	8	-3	0	5	1	0	-10	0	6	-3	-4	1	15	4	-2	6	-9	-7

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Quadratic twists for elliptic curve 7744h2

-4	8	-3	-11
7744x2	484a2	69696di2	704d2

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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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