Cremona's table of elliptic curves

192 = 2⁶ · 3

Field	Data	Notes
Atkin-Lehner	2- 3+	Signs for the Atkin-Lehner involutions
Class	192d	Isogeny class
Conductor	192	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-3072 = -1 · 210 · 3	Discriminant
Eigenvalues	2- 3+  2  0  4  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,3,-3]	[a1,a2,a3,a4,a6]
j	2048/3	j-invariant
L	1.1920055072756	L(r)(E,1)/r!
Ω	2.3840110145512	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	192c1 48a4 576i1 4800cb1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 192d1

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

---

Quadratic twists for elliptic curve 192d1

-4	8	-3	5	-7	-11	13	17	-19	-23
192c1	48a4	576i1	4800cb1	9408cz1	23232cz1	32448ci1	55488du1	69312dl1	101568cm1

---

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