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	126a	Isogeny class
Conductor	126	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-20412 = -1 · 22 · 36 · 7	Discriminant
Eigenvalues	2- 3-  0 7-  0 -4 -6  2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-5,-7]	[a1,a2,a3,a4,a6]
j	-15625/28	j-invariant
L	1.5305454480783	L(r)(E,1)/r!
Ω	1.5305454480783	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	1008i1 4032l1 14a4 3150l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 126a1

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

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Quadratic twists for elliptic curve 126a1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
1008i1	4032l1	14a4	3150l1	882i1	15246i1	21294o1	36414cf1	45486p1	66654bi1	105966u1	121086bc1

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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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