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	11638n	Isogeny class
Conductor	11638	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-512072 = -1 · 23 · 112 · 232	Discriminant
Eigenvalues	2+ -3  0  0 11-  2  1  5	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-7,37]	[a1,a2,a3,a4,a6]
Generators	[1:5:1]	Generators of the group modulo torsion
j	-77625/968	j-invariant
L	2.1236734398052	L(r)(E,1)/r!
Ω	2.4925177525837	Real period
R	0.42600969192773	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	93104t1 104742bk1 128018bm1 11638g1	Quadratic twists by: -4 -3 -11 -23

Hecke Eigenvalues for elliptic curve 11638n1

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	0	0	-	2	1	5	-	6	10	-6	-2	-1	-10	-4	-3	12	-3	-4	1	8	-5	-14	2

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Quadratic twists for elliptic curve 11638n1

-4	-3	-11	-23
93104t1	104742bk1	128018bm1	11638g1

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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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