Cremona's table of elliptic curves

4719 = 3 · 11² · 13

Field	Data	Notes
Atkin-Lehner	3- 11- 13+	Signs for the Atkin-Lehner involutions
Class	4719k	Isogeny class
Conductor	4719	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	3360	Modular degree for the optimal curve
Δ	-44721963 = -1 · 37 · 112 · 132	Discriminant
Eigenvalues	-2 3- -2 -3 11- 13+  0  1	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-1184,15296]	[a1,a2,a3,a4,a6]
Generators	[22:-20:1]	Generators of the group modulo torsion
j	-1518309117952/369603	j-invariant
L	1.754744202391	L(r)(E,1)/r!
Ω	1.9724466083184	Real period
R	0.063544874203828	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	75504bm1 14157o1 117975s1 4719m1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 4719k1

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	-	-2	-3	-	+	0	1	4	-8	9	9	2	-4	2	2	6	-11	-15	6	9	1	0	8	7

---

Quadratic twists for elliptic curve 4719k1

-4	-3	5	-11	13
75504bm1	14157o1	117975s1	4719m1	61347bc1

---

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