Cremona's table of elliptic curves

3486 = 2 · 3 · 7 · 83

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 83-	Signs for the Atkin-Lehner involutions
Class	3486q	Isogeny class
Conductor	3486	Conductor
∏ cp	180	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	-81971979264 = -1 · 210 · 39 · 72 · 83	Discriminant
Eigenvalues	2- 3- -1 7- -1 -4 -6 -5	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-8546,303684]	[a1,a2,a3,a4,a6]
Generators	[58:-92:1]	Generators of the group modulo torsion
j	-69026452436759329/81971979264	j-invariant
L	5.5587236804971	L(r)(E,1)/r!
Ω	1.0782155398362	Real period
R	0.02864158146865	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	27888o1 111552r1 10458n1 87150b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3486q1

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	-	-1	-4	-6	-5	-3	-10	-2	-3	10	-4	6	-3	15	-5	-5	4	8	8	-	-5	16

---

Quadratic twists for elliptic curve 3486q1

-4	8	-3	5	-7
27888o1	111552r1	10458n1	87150b1	24402p1

---

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