Cremona's table of elliptic curves

8085 = 3 · 5 · 7² · 11

Field	Data	Notes
Atkin-Lehner	3- 5- 7- 11+	Signs for the Atkin-Lehner involutions
Class	8085w	Isogeny class
Conductor	8085	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-22607799493125 = -1 · 3 · 54 · 77 · 114	Discriminant
Eigenvalues	-1 3- 5- 7- 11+  2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,2400,-224043]	[a1,a2,a3,a4,a6]
j	12994449551/192163125	j-invariant
L	1.3248420925197	L(r)(E,1)/r!
Ω	0.33121052312992	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	129360fk3 24255bh3 40425j3 1155a4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8085w4

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	-6	-4	0	-6	0	6	10	4	-8	-6	8	-2	-8	-8	14	4	16	10	2

---

Quadratic twists for elliptic curve 8085w4

-4	-3	5	-7	-11
129360fk3	24255bh3	40425j3	1155a4	88935cg3

---

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