Cremona's table of elliptic curves

17136 = 2⁴ · 3² · 7 · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 17-	Signs for the Atkin-Lehner involutions
Class	17136q	Isogeny class
Conductor	17136	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	1920	Modular degree for the optimal curve
Δ	873936 = 24 · 33 · 7 · 172	Discriminant
Eigenvalues	2- 3+  2 7+  2  2 17-  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-24,-5]	[a1,a2,a3,a4,a6]
Generators	[-14:45:8]	Generators of the group modulo torsion
j	3538944/2023	j-invariant
L	5.9511531665909	L(r)(E,1)/r!
Ω	2.3366359874312	Real period
R	2.5468892881058	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4284d1 68544cy1 17136n1 119952cp1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 17136q1

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	+	2	2	-	6	-6	-6	-4	2	6	-12	-8	4	-12	0	-4	-2	-16	0	4	-10	12

---

Quadratic twists for elliptic curve 17136q1

-4	8	-3	-7
4284d1	68544cy1	17136n1	119952cp1

---

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