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	2	Product of Tamagawa factors cp
Δ	3174 = 2 · 3 · 232	Discriminant
Eigenvalues	2+ 3+ -2 -2 -6 -2  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-31,55]	[a1,a2,a3,a4,a6]
Generators	[-3:13:1]	Generators of the group modulo torsion
j	3463512697/3174	j-invariant
L	0.79077129713144	L(r)(E,1)/r!
Ω	4.4583602683019	Real period
R	0.35473638268027	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	1104i2 4416h2 414b2 3450x2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 138a2

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 138a2

-4	8	-3	5	-7	-11	13	17	-19	-23	29
1104i2	4416h2	414b2	3450x2	6762o2	16698ba2	23322l2	39882w2	49818bf2	3174a2	116058bd2

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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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