Cremona's table of elliptic curves

16320 = 2⁶ · 3 · 5 · 17

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 17-	Signs for the Atkin-Lehner involutions
Class	16320f	Isogeny class
Conductor	16320	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	41779200 = 215 · 3 · 52 · 17	Discriminant
Eigenvalues	2+ 3+ 5+  0 -4 -6 17- -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-54401,4901985]	[a1,a2,a3,a4,a6]
Generators	[-107:3080:1] [-27:2520:1]	Generators of the group modulo torsion
j	543378448339208/1275	j-invariant
L	5.6619653625278	L(r)(E,1)/r!
Ω	1.3322860363984	Real period
R	8.4996242666239	Regulator
r	2	Rank of the group of rational points
S	0.99999999999995	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	16320ba3 8160f3 48960cm4 81600cp4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 16320f3

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	-6	-	-4	-4	-6	0	-2	-6	4	0	-10	-4	-2	-4	12	2	-16	-4	-6	-14

---

Quadratic twists for elliptic curve 16320f3

-4	8	-3	5
16320ba3	8160f3	48960cm4	81600cp4

---

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