Cremona's table of elliptic curves

3168 = 2⁵ · 3² · 11

Field	Data	Notes
Atkin-Lehner	2+ 3- 11+	Signs for the Atkin-Lehner involutions
Class	3168k	Isogeny class
Conductor	3168	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-406467072 = -1 · 29 · 38 · 112	Discriminant
Eigenvalues	2+ 3-  4  2 11+  4 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-3,-970]	[a1,a2,a3,a4,a6]
j	-8/1089	j-invariant
L	3.0779732820011	L(r)(E,1)/r!
Ω	0.76949332050029	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	3168bb2 6336bf2 1056h2 79200dl2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3168k2

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
+	-	4	2	+	4	-2	-4	6	6	-4	-2	-6	-8	10	12	0	8	-4	6	10	6	-12	14	-18

---

Quadratic twists for elliptic curve 3168k2

-4	8	-3	5	-11
3168bb2	6336bf2	1056h2	79200dl2	34848ck2

---

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