Cremona's table of elliptic curves

17760 = 2⁵ · 3 · 5 · 37

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 37-	Signs for the Atkin-Lehner involutions
Class	17760z	Isogeny class
Conductor	17760	Conductor
∏ cp	30	Product of Tamagawa factors cp
deg	9600	Modular degree for the optimal curve
Δ	-4603392000 = -1 · 212 · 35 · 53 · 37	Discriminant
Eigenvalues	2- 3- 5- -2  6 -5  4 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,35,3275]	[a1,a2,a3,a4,a6]
Generators	[5:60:1]	Generators of the group modulo torsion
j	1124864/1123875	j-invariant
L	6.4332356581078	L(r)(E,1)/r!
Ω	1.074545292034	Real period
R	0.19956458810376	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	17760i1 35520c1 53280n1 88800d1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17760z1

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	6	-5	4	-4	2	-5	-4	-	-2	3	-9	1	-9	0	4	-2	-4	-12	-7	-3	6

---

Quadratic twists for elliptic curve 17760z1

-4	8	-3	5
17760i1	35520c1	53280n1	88800d1

---

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