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	8085p	Isogeny class
Conductor	8085	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	1678602105301275 = 32 · 52 · 714 · 11	Discriminant
Eigenvalues	-1 3- 5+ 7- 11-  2  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-649251,201293406]	[a1,a2,a3,a4,a6]
j	257260669489908001/14267882475	j-invariant
L	1.7889190259759	L(r)(E,1)/r!
Ω	0.44722975649398	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	129360du6 24255bm6 40425w6 1155e5	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8085p5

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	8	6	-8	6	6	-4	8	-10	12	10	-12	-8	6	8	4	-10	14

---

Quadratic twists for elliptic curve 8085p5

-4	-3	5	-7	-11
129360du6	24255bm6	40425w6	1155e5	88935bq6

---

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