Cremona's table of elliptic curves

4599 = 3² · 7 · 73

Field	Data	Notes
Atkin-Lehner	3+ 7- 73-	Signs for the Atkin-Lehner involutions
Class	4599a	Isogeny class
Conductor	4599	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	1440	Modular degree for the optimal curve
Δ	-492842637 = -1 · 39 · 73 · 73	Discriminant
Eigenvalues	1 3+  2 7-  4 -3 -4 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-231,-1666]	[a1,a2,a3,a4,a6]
Generators	[70:532:1]	Generators of the group modulo torsion
j	-69426531/25039	j-invariant
L	5.1364764040245	L(r)(E,1)/r!
Ω	0.60130974211658	Real period
R	1.4236912205303	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	73584n1 4599b1 114975b1 32193a1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4599a1

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	-3	-4	-1	-5	-7	-8	9	-3	-5	0	1	-3	-8	8	-9	-	8	-5	3	-10

---

Quadratic twists for elliptic curve 4599a1

-4	-3	5	-7
73584n1	4599b1	114975b1	32193a1

---

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