Cremona's table of elliptic curves

17040 = 2⁴ · 3 · 5 · 71

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 71-	Signs for the Atkin-Lehner involutions
Class	17040bd	Isogeny class
Conductor	17040	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	41812070400 = 212 · 34 · 52 · 712	Discriminant
Eigenvalues	2- 3- 5- -4 -4  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1920,-31500]	[a1,a2,a3,a4,a6]
Generators	[-22:24:1]	Generators of the group modulo torsion
j	191202526081/10208025	j-invariant
L	5.3562278411484	L(r)(E,1)/r!
Ω	0.7235959677986	Real period
R	1.8505589028653	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	1065b2 68160cf2 51120bd2 85200ch2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 17040bd2

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
-	-	-	-4	-4	2	-2	4	-4	-2	0	-2	10	4	4	10	-4	6	8	-	-6	-8	4	10	-10

---

Quadratic twists for elliptic curve 17040bd2

-4	8	-3	5
1065b2	68160cf2	51120bd2	85200ch2

---

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