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	138a	Isogeny class
Conductor	138	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-828 = -1 · 22 · 32 · 23	Discriminant
Eigenvalues	2+ 3+ -2 -2 -6 -2  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-1,1]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	-389017/828	j-invariant
L	0.79077129713144	L(r)(E,1)/r!
Ω	4.4583602683019	Real period
R	0.17736819134014	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1104i1 4416h1 414b1 3450x1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 138a1

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	-2	-6	-2	0	0	+	6	8	0	10	-12	-8	2	-12	4	-12	0	-10	-6	14	0	-6

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Quadratic twists for elliptic curve 138a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29
1104i1	4416h1	414b1	3450x1	6762o1	16698ba1	23322l1	39882w1	49818bf1	3174a1	116058bd1

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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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