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	11638m	Isogeny class
Conductor	11638	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	123648	Modular degree for the optimal curve
Δ	-2293102270998242 = -1 · 2 · 114 · 238	Discriminant
Eigenvalues	2+  3  2 -2 11- -4 -3 -5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,32699,-366721]	[a1,a2,a3,a4,a6]
Generators	[975:24554:27]	Generators of the group modulo torsion
j	49373847/29282	j-invariant
L	6.1190666559891	L(r)(E,1)/r!
Ω	0.26960554772899	Real period
R	5.6740919349888	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	93104u1 104742bu1 128018bh1 11638f1	Quadratic twists by: -4 -3 -11 -23

Hecke Eigenvalues for elliptic curve 11638m1

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
+	3	2	-2	-	-4	-3	-5	-	0	-2	-2	-10	5	2	-12	7	8	1	14	11	-16	-15	-2	-14

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Quadratic twists for elliptic curve 11638m1

-4	-3	-11	-23
93104u1	104742bu1	128018bh1	11638f1

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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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