Cremona's table of elliptic curves

11638 = 2 · 11 · 23²

Field	Data	Notes
Atkin-Lehner	2+ 11- 23-	Signs for the Atkin-Lehner involutions
Class	11638l	Isogeny class
Conductor	11638	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	29568	Modular degree for the optimal curve
Δ	4793994229376 = 27 · 11 · 237	Discriminant
Eigenvalues	2+ -2 -1  1 11-  3 -3  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-25139,1528398]	[a1,a2,a3,a4,a6]
Generators	[136:725:1]	Generators of the group modulo torsion
j	11867954041/32384	j-invariant
L	2.2183408041024	L(r)(E,1)/r!
Ω	0.77311373671129	Real period
R	0.71733973242373	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	93104q1 104742bn1 128018ba1 506a1	Quadratic twists by: -4 -3 -11 -23

Hecke Eigenvalues for elliptic curve 11638l1

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	1	-	3	-3	6	-	-1	-7	5	-2	8	-1	6	-10	8	-7	-5	4	-11	-12	-6	-2

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Quadratic twists for elliptic curve 11638l1

-4	-3	-11	-23
93104q1	104742bn1	128018ba1	506a1

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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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