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	4	Product of Tamagawa factors cp
Δ	680811468498 = 2 · 310 · 78	Discriminant
Eigenvalues	2+ 3-  2 7+  4  6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-8226,286474]	[a1,a2,a3,a4,a6]
j	84448510979617/933897762	j-invariant
L	0.91047373686993	L(r)(E,1)/r!
Ω	0.91047373686993	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	1008l5 4032i5 42a5 3150bl5	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 126b5

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 126b5

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
1008l5	4032i5	42a5	3150bl5	882e5	15246bs5	21294cm6	36414bi6	45486bh6	66654w6	105966bu6	121086g6

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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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