Cremona's table of elliptic curves

5538 = 2 · 3 · 13 · 71

Field	Data	Notes
Atkin-Lehner	2- 3- 13+ 71+	Signs for the Atkin-Lehner involutions
Class	5538p	Isogeny class
Conductor	5538	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	448	Modular degree for the optimal curve
Δ	-71994 = -1 · 2 · 3 · 132 · 71	Discriminant
Eigenvalues	2- 3- -1 -1 -3 13+ -2  1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-1,-13]	[a1,a2,a3,a4,a6]
Generators	[38:59:8]	Generators of the group modulo torsion
j	-117649/71994	j-invariant
L	6.1237538445067	L(r)(E,1)/r!
Ω	1.5555113890242	Real period
R	1.9684053385004	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	44304d1 16614i1 71994u1	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 5538p1

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	+	-2	1	6	-3	-1	-6	1	-1	-8	-10	3	11	-8	+	7	-10	-10	16	0

---

Quadratic twists for elliptic curve 5538p1

-4	-3	13
44304d1	16614i1	71994u1

---

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