Cremona's table of elliptic curves

4165 = 5 · 7² · 17

Field	Data	Notes
Atkin-Lehner	5- 7- 17+	Signs for the Atkin-Lehner involutions
Class	4165k	Isogeny class
Conductor	4165	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	10080	Modular degree for the optimal curve
Δ	-24782158898875 = -1 · 53 · 79 · 173	Discriminant
Eigenvalues	-2  0 5- 7- -2 -3 17+  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,343,-239500]	[a1,a2,a3,a4,a6]
Generators	[98:857:1]	Generators of the group modulo torsion
j	110592/614125	j-invariant
L	1.7941223071522	L(r)(E,1)/r!
Ω	0.31099408420961	Real period
R	0.96149862556176	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	66640bx1 37485bf1 20825t1 4165g1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 4165k1

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
-2	0	-	-	-2	-3	+	0	-1	8	9	3	3	6	3	-4	-6	-15	4	-2	6	-10	15	0	-12

---

Quadratic twists for elliptic curve 4165k1

-4	-3	5	-7	17
66640bx1	37485bf1	20825t1	4165g1	70805p1

---

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