Cremona's table of elliptic curves

6783 = 3 · 7 · 17 · 19

Field	Data	Notes
Atkin-Lehner	3- 7+ 17+ 19-	Signs for the Atkin-Lehner involutions
Class	6783c	Isogeny class
Conductor	6783	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	18880	Modular degree for the optimal curve
Δ	-225449504735679 = -1 · 35 · 7 · 178 · 19	Discriminant
Eigenvalues	-1 3-  2 7+  0  2 17+ 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-27167,-1871040]	[a1,a2,a3,a4,a6]
Generators	[24845:83693:125]	Generators of the group modulo torsion
j	-2217429186346572913/225449504735679	j-invariant
L	3.5079257145409	L(r)(E,1)/r!
Ω	0.1848695667595	Real period
R	7.5900555749218	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	108528s1 20349g1 47481i1 115311j1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 6783c1

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
-1	-	2	+	0	2	+	-	-4	-2	0	-2	2	-12	-8	6	4	-10	-8	-8	-14	12	-4	10	-2

---

Quadratic twists for elliptic curve 6783c1

-4	-3	-7	17	-19
108528s1	20349g1	47481i1	115311j1	128877a1

---

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