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	8	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-3312 = -1 · 24 · 32 · 23	Discriminant
Eigenvalues	2- 3+  2  0  0 -2  2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,3,3]	[a1,a2,a3,a4,a6]
j	2924207/3312	j-invariant
L	1.4877307684125	L(r)(E,1)/r!
Ω	2.9754615368251	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1104h1 4416i1 414c1 3450i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 138c1

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 138c1

-4	8	-3	5	-7	-11	13	17	-19	-23	29
1104h1	4416i1	414c1	3450i1	6762bi1	16698e1	23322b1	39882bt1	49818k1	3174g1	116058g1

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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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