Cremona's table of elliptic curves

11726 = 2 · 11 · 13 · 41

Field	Data	Notes
Atkin-Lehner	2+ 11- 13+ 41+	Signs for the Atkin-Lehner involutions
Class	11726d	Isogeny class
Conductor	11726	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	-78048256 = -1 · 210 · 11 · 132 · 41	Discriminant
Eigenvalues	2+ -2  1 -3 11- 13+  5 -7	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-8,-426]	[a1,a2,a3,a4,a6]
Generators	[8:2:1] [9:11:1]	Generators of the group modulo torsion
j	-47045881/78048256	j-invariant
L	3.6029367672643	L(r)(E,1)/r!
Ω	0.87362955515436	Real period
R	1.031025320174	Regulator
r	2	Rank of the group of rational points
S	0.99999999999951	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	93808u1 105534bd1 128986be1	Quadratic twists by: -4 -3 -11

Hecke Eigenvalues for elliptic curve 11726d1

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
+	-2	1	-3	-	+	5	-7	-7	-9	-7	-11	+	-10	-10	12	3	12	2	2	-16	-8	16	4	0

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Quadratic twists for elliptic curve 11726d1

-4	-3	-11
93808u1	105534bd1	128986be1

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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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