Cremona's table of elliptic curves

9537 = 3 · 11 · 17²

Field	Data	Notes
Atkin-Lehner	3+ 11- 17+	Signs for the Atkin-Lehner involutions
Class	9537f	Isogeny class
Conductor	9537	Conductor
∏ cp	6	Product of Tamagawa factors cp
deg	6048	Modular degree for the optimal curve
Δ	-280416411 = -1 · 36 · 113 · 172	Discriminant
Eigenvalues	0 3+ -3 -2 11- -4 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-1847,31187]	[a1,a2,a3,a4,a6]
Generators	[-49:40:1] [5:148:1]	Generators of the group modulo torsion
j	-2412468600832/970299	j-invariant
L	3.6907789583724	L(r)(E,1)/r!
Ω	1.7067728070294	Real period
R	0.36040521846968	Regulator
r	2	Rank of the group of rational points
S	0.99999999999978	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	28611g1 104907i1 9537k1	Quadratic twists by: -3 -11 17

Hecke Eigenvalues for elliptic curve 9537f1

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
0	+	-3	-2	-	-4	+	-4	9	-6	1	-2	-6	-10	3	-6	-12	4	-7	-3	-2	-8	-6	9	-17

---

Quadratic twists for elliptic curve 9537f1

-3	-11	17
28611g1	104907i1	9537k1

---

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