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	11638r	Isogeny class
Conductor	11638	Conductor
∏ cp	18	Product of Tamagawa factors cp
deg	278208	Modular degree for the optimal curve
Δ	1227435106512513536 = 29 · 113 · 239	Discriminant
Eigenvalues	2- -2  3  3 11+ -5 -3  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-273504,-13796864]	[a1,a2,a3,a4,a6]
Generators	[2160:96256:1]	Generators of the group modulo torsion
j	1256216039/681472	j-invariant
L	6.1905324813992	L(r)(E,1)/r!
Ω	0.22260102490598	Real period
R	1.5449994955509	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	93104be1 104742bc1 128018m1 11638v1	Quadratic twists by: -4 -3 -11 -23

Hecke Eigenvalues for elliptic curve 11638r1

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	3	3	+	-5	-3	0	-	-9	-5	9	0	0	-3	6	-12	0	15	-15	-2	3	0	-12	6

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Quadratic twists for elliptic curve 11638r1

-4	-3	-11	-23
93104be1	104742bc1	128018m1	11638v1

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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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