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	11638k	Isogeny class
Conductor	11638	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2496	Modular degree for the optimal curve
Δ	267674 = 2 · 11 · 233	Discriminant
Eigenvalues	2+  2  1 -1 11-  5 -7  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-137,563]	[a1,a2,a3,a4,a6]
Generators	[13:28:1]	Generators of the group modulo torsion
j	23639903/22	j-invariant
L	5.1272003907601	L(r)(E,1)/r!
Ω	3.0814224088896	Real period
R	0.83195351211321	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	93104s1 104742bt1 128018y1 11638d1	Quadratic twists by: -4 -3 -11 -23

Hecke Eigenvalues for elliptic curve 11638k1

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	-	5	-7	4	-	1	-5	-5	0	-12	5	10	-4	-4	-3	9	-6	-9	-4	-12	6

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Quadratic twists for elliptic curve 11638k1

-4	-3	-11	-23
93104s1	104742bt1	128018y1	11638d1

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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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