Cremona's table of elliptic curves

8092 = 2² · 7 · 17²

Field	Data	Notes
Atkin-Lehner	2- 7- 17-	Signs for the Atkin-Lehner involutions
Class	8092h	Isogeny class
Conductor	8092	Conductor
∏ cp	45	Product of Tamagawa factors cp
deg	8640	Modular degree for the optimal curve
Δ	359356786432 = 28 · 75 · 174	Discriminant
Eigenvalues	2- -1 -2 7- -4 -4 17- -3	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3564,77848]	[a1,a2,a3,a4,a6]
Generators	[-62:238:1] [6:238:1]	Generators of the group modulo torsion
j	234219472/16807	j-invariant
L	4.4248410041655	L(r)(E,1)/r!
Ω	0.93708487955565	Real period
R	0.1049315832939	Regulator
r	2	Rank of the group of rational points
S	1.0000000000002	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	32368o1 129472bl1 72828bc1 56644q1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8092h1

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	-	-4	-4	-	-3	-6	3	-5	-10	-6	-6	-5	5	3	-6	10	-14	-10	12	-5	-2	-12

---

Quadratic twists for elliptic curve 8092h1

-4	8	-3	-7	17
32368o1	129472bl1	72828bc1	56644q1	8092a1

---

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