Cremona's table of elliptic curves

3509 = 11² · 29

Field	Data	Notes
Atkin-Lehner	11- 29+	Signs for the Atkin-Lehner involutions
Class	3509c	Isogeny class
Conductor	3509	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	11040	Modular degree for the optimal curve
Δ	-16388710811 = -1 · 117 · 292	Discriminant
Eigenvalues	-2 -3  1 -4 11- -6 -4  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-4477,115464]	[a1,a2,a3,a4,a6]
Generators	[-1080260290112655461568:-18767486957424528238335:40321109308918660039] [9:275:1]	Generators of the group modulo torsion
j	-5601816576/9251	j-invariant
L	1.5589947907909	L(r)(E,1)/r!
Ω	1.2367282086007	Real period
R	0.15757249450142	Regulator
r	2	Rank of the group of rational points
S	0.99999999999681	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	56144o1 31581n1 87725g1 319a1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 3509c1

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	-3	1	-4	-	-6	-4	2	3	+	-7	-11	-4	4	8	2	-3	-2	-15	-7	-2	-6	6	9	-17

---

Quadratic twists for elliptic curve 3509c1

-4	-3	5	-11	29
56144o1	31581n1	87725g1	319a1	101761g1

---

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