Cremona's table of elliptic curves

10710 = 2 · 3² · 5 · 7 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7+ 17+	Signs for the Atkin-Lehner involutions
Class	10710x	Isogeny class
Conductor	10710	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-3196557472500 = -1 · 22 · 37 · 54 · 7 · 174	Discriminant
Eigenvalues	2- 3- 5+ 7+ -4  2 17+ -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,2677,66831]	[a1,a2,a3,a4,a6]
Generators	[35:432:1]	Generators of the group modulo torsion
j	2911343039639/4384852500	j-invariant
L	6.0034091042913	L(r)(E,1)/r!
Ω	0.5415134368377	Real period
R	1.3857941225221	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	85680ej3 3570g4 53550cb3 74970eb3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 10710x4

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
-	-	+	+	-4	2	+	-4	8	6	-8	6	-2	0	4	14	-12	-6	-8	-16	2	-4	8	-10	10

---

Quadratic twists for elliptic curve 10710x4

-4	-3	5	-7
85680ej3	3570g4	53550cb3	74970eb3

---

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