Cremona's table of elliptic curves

13520 = 2⁴ · 5 · 13²

Field	Data	Notes
Atkin-Lehner	2- 5+ 13+	Signs for the Atkin-Lehner involutions
Class	13520q	Isogeny class
Conductor	13520	Conductor
∏ cp	6	Product of Tamagawa factors cp
Δ	203932680250000 = 24 · 56 · 138	Discriminant
Eigenvalues	2- -1 5+  1 -3 13+ -3 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-49066,4142891]	[a1,a2,a3,a4,a6]
Generators	[113:169:1] [161:625:1]	Generators of the group modulo torsion
j	1000939264/15625	j-invariant
L	5.4326063734416	L(r)(E,1)/r!
Ω	0.5649715931615	Real period
R	1.6026193290659	Regulator
r	2	Rank of the group of rational points
S	0.99999999999979	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3380b2 54080cx2 121680er2 67600bo2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 13520q2

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
-	-1	+	1	-3	+	-3	-5	-9	-9	-8	-7	3	1	0	6	-9	-1	-5	-9	2	-8	0	3	17

---

Quadratic twists for elliptic curve 13520q2

-4	8	-3	5	13
3380b2	54080cx2	121680er2	67600bo2	13520z2

---

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