Cremona's table of elliptic curves

8736 = 2⁵ · 3 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 13+	Signs for the Atkin-Lehner involutions
Class	8736h	Isogeny class
Conductor	8736	Conductor
∏ cp	38	Product of Tamagawa factors cp
deg	18240	Modular degree for the optimal curve
Δ	-54152086270464 = -1 · 29 · 319 · 7 · 13	Discriminant
Eigenvalues	2+ 3- -1 7- -1 13+ -5  3	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-12696,-658872]	[a1,a2,a3,a4,a6]
Generators	[138:486:1]	Generators of the group modulo torsion
j	-442067613591752/105765793497	j-invariant
L	4.9556868868644	L(r)(E,1)/r!
Ω	0.22206993134152	Real period
R	0.58726011227364	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	8736l1 17472k1 26208bo1 61152i1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 8736h1

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	+	-5	3	7	-5	-4	3	0	5	0	-6	-4	5	-6	-8	1	-10	-6	14	-18

---

Quadratic twists for elliptic curve 8736h1

-4	8	-3	-7	13
8736l1	17472k1	26208bo1	61152i1	113568ck1

---

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