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	-3075343841682 = -1 · 2 · 322 · 72	Discriminant
Eigenvalues	2+ 3-  2 7+  4  6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,3474,-31010]	[a1,a2,a3,a4,a6]
j	6359387729183/4218578658	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	1008l6 4032i6 42a6 3150bl6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 126b6

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

---

Quadratic twists for elliptic curve 126b6

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31
1008l6	4032i6	42a6	3150bl6	882e6	15246bs6	21294cm5	36414bi5	45486bh5	66654w5	105966bu5	121086g5

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations