Cremona's table of elliptic curves

6392 = 2³ · 17 · 47

Field	Data	Notes
Atkin-Lehner	2- 17+ 47-	Signs for the Atkin-Lehner involutions
Class	6392b	Isogeny class
Conductor	6392	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	27817984 = 211 · 172 · 47	Discriminant
Eigenvalues	2-  0 -2 -2  2  6 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2011,34710]	[a1,a2,a3,a4,a6]
Generators	[42:156:1]	Generators of the group modulo torsion
j	439167275874/13583	j-invariant
L	3.2563832641807	L(r)(E,1)/r!
Ω	1.9620107029638	Real period
R	3.3194347607397	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	12784a2 51136b2 57528f2 108664b2	Quadratic twists by: -4 8 -3 17

Hecke Eigenvalues for elliptic curve 6392b2

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
-	0	-2	-2	2	6	+	0	-4	2	4	4	-4	4	-	2	12	-4	-12	-2	4	-2	12	-10	-10

---

Quadratic twists for elliptic curve 6392b2

-4	8	-3	17
12784a2	51136b2	57528f2	108664b2

---

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