Cremona's table of elliptic curves

5187 = 3 · 7 · 13 · 19

Field	Data	Notes
Atkin-Lehner	3- 7+ 13+ 19-	Signs for the Atkin-Lehner involutions
Class	5187d	Isogeny class
Conductor	5187	Conductor
∏ cp	24	Product of Tamagawa factors cp
Δ	315169490727 = 312 · 74 · 13 · 19	Discriminant
Eigenvalues	1 3- -2 7+  4 13+  2 19-	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-2062,23669]	[a1,a2,a3,a4,a6]
Generators	[-23:254:1]	Generators of the group modulo torsion
j	968917714969177/315169490727	j-invariant
L	4.8160275625259	L(r)(E,1)/r!
Ω	0.89231114315033	Real period
R	0.89954189923833	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	82992bw3 15561d3 129675o3 36309g3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 5187d4

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	-	-2	+	4	+	2	-	-4	2	8	-6	-2	4	-8	2	0	-10	-8	0	-10	-8	-12	-10	14

---

Quadratic twists for elliptic curve 5187d4

-4	-3	5	-7	13	-19
82992bw3	15561d3	129675o3	36309g3	67431p3	98553h3

---

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