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	138b	Isogeny class
Conductor	138	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-448524288 = -1 · 212 · 32 · 233	Discriminant
Eigenvalues	2+ 3-  0  2  0  2  0  2	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,189,190]	[a1,a2,a3,a4,a6]
j	752329532375/448524288	j-invariant
L	1.0200678073909	L(r)(E,1)/r!
Ω	1.0200678073909	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	1104g3 4416a3 414a3 3450r3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 138b3

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
+	-	0	2	0	2	0	2	+	-6	-4	-10	-6	2	0	12	12	-10	14	0	2	-10	0	12	-10

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Quadratic twists for elliptic curve 138b3

-4	8	-3	5	-7	-11	13	17	-19	-23	29
1104g3	4416a3	414a3	3450r3	6762b3	16698bl3	23322t3	39882f3	49818y3	3174d3	116058r3

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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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