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	8	Product of Tamagawa factors cp
Δ	5308416 = 216 · 34	Discriminant
Eigenvalues	2- 3+  2  0  4  2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-97,385]	[a1,a2,a3,a4,a6]
j	1556068/81	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	4	Number of elements in the torsion subgroup
Twists	192c3 48a3 576i3 4800cb4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 192d4

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 192d4

-4	8	-3	5	-7	-11	13	17	-19	-23
192c3	48a3	576i3	4800cb4	9408cz3	23232cz3	32448ci3	55488du3	69312dl3	101568cm3

---

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