Cremona's table of elliptic curves

126 = 2 · 3² · 7

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+	Signs for the Atkin-Lehner involutions
Class	126b	Isogeny class
Conductor	126	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	183708 = 22 · 38 · 7	Discriminant
Eigenvalues	2+ 3-  2 7+  4  6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-12096,-509036]	[a1,a2,a3,a4,a6]
j	268498407453697/252	j-invariant
L	0.91047373686993	L(r)(E,1)/r!
Ω	0.45523686843496	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	1008l4 4032i3 42a4 3150bl3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 126b3

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

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Quadratic twists for elliptic curve 126b3

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
1008l4	4032i3	42a4	3150bl3	882e4	15246bs4	21294cm4	36414bi4	45486bh4	66654w4	105966bu4	121086g4

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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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