Cremona's table of elliptic curves

16992 = 2⁵ · 3² · 59

Field	Data	Notes
Atkin-Lehner	2- 3- 59+	Signs for the Atkin-Lehner involutions
Class	16992g	Isogeny class
Conductor	16992	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	4096	Modular degree for the optimal curve
Δ	8258112 = 26 · 37 · 59	Discriminant
Eigenvalues	2- 3-  0 -4 -4 -4  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-525,4628]	[a1,a2,a3,a4,a6]
Generators	[7:36:1]	Generators of the group modulo torsion
j	343000000/177	j-invariant
L	3.6605599969803	L(r)(E,1)/r!
Ω	2.2980692027551	Real period
R	0.79644250760415	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	16992c1 33984s1 5664b1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 16992g1

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

---

Quadratic twists for elliptic curve 16992g1

-4	8	-3
16992c1	33984s1	5664b1

---

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