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
deg	32	Modular degree for the optimal curve
Δ	-11757312 = -1 · 28 · 38 · 7	Discriminant
Eigenvalues	2+ 3-  2 7+  4  6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-36,-176]	[a1,a2,a3,a4,a6]
j	-7189057/16128	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	1008l1 4032i1 42a1 3150bl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 126b1

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 126b1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
1008l1	4032i1	42a1	3150bl1	882e1	15246bs1	21294cm1	36414bi1	45486bh1	66654w1	105966bu1	121086g1

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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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