Cremona's table of elliptic curves

138 = 2 · 3 · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 23+	Signs for the Atkin-Lehner involutions
Class	138c	Isogeny class
Conductor	138	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	5037138 = 2 · 32 · 234	Discriminant
Eigenvalues	2- 3+  2  0  0 -2  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-107,-457]	[a1,a2,a3,a4,a6]
j	135559106353/5037138	j-invariant
L	1.4877307684125	L(r)(E,1)/r!
Ω	1.4877307684125	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1104h4 4416i3 414c4 3450i3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 138c3

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	0	0	-2	2	-8	+	-2	-8	2	10	8	8	2	-4	2	8	0	-6	8	-16	18	10

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Quadratic twists for elliptic curve 138c3

-4	8	-3	5	-7	-11	13	17	-19	-23	29
1104h4	4416i3	414c4	3450i3	6762bi4	16698e4	23322b3	39882bt3	49818k3	3174g4	116058g3

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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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