Cremona's table of elliptic curves

6192 = 2⁴ · 3² · 43

Field	Data	Notes
Atkin-Lehner	2+ 3+ 43+	Signs for the Atkin-Lehner involutions
Class	6192b	Isogeny class
Conductor	6192	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-37267319808 = -1 · 210 · 39 · 432	Discriminant
Eigenvalues	2+ 3+ -2 -4  2  2 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,189,9234]	[a1,a2,a3,a4,a6]
Generators	[9:108:1]	Generators of the group modulo torsion
j	37044/1849	j-invariant
L	3.083094612017	L(r)(E,1)/r!
Ω	0.87732106577933	Real period
R	0.87855368241907	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3096g2 24768br2 6192a2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 6192b2

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

---

Quadratic twists for elliptic curve 6192b2

-4	8	-3
3096g2	24768br2	6192a2

---

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