Cremona's table of elliptic curves

8710 = 2 · 5 · 13 · 67

Field	Data	Notes
Atkin-Lehner	2+ 5+ 13+ 67+	Signs for the Atkin-Lehner involutions
Class	8710a	Isogeny class
Conductor	8710	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	353843750 = 2 · 56 · 132 · 67	Discriminant
Eigenvalues	2+  2 5+  0 -2 13+ -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-748,-8142]	[a1,a2,a3,a4,a6]
Generators	[-429:400:27]	Generators of the group modulo torsion
j	46380496070089/353843750	j-invariant
L	4.1030896986641	L(r)(E,1)/r!
Ω	0.91316308472443	Real period
R	4.493271538569	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	69680r2 78390bu2 43550x2 113230x2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 8710a2

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

---

Quadratic twists for elliptic curve 8710a2

-4	-3	5	13
69680r2	78390bu2	43550x2	113230x2

---

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