Cremona's table of elliptic curves

8470 = 2 · 5 · 7 · 11²

Field	Data	Notes
Atkin-Lehner	2- 5+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	8470v	Isogeny class
Conductor	8470	Conductor
∏ cp	336	Product of Tamagawa factors cp
Δ	64139599462400 = 214 · 52 · 76 · 113	Discriminant
Eigenvalues	2-  0 5+ 7- 11+ -4  4  4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-961588,363177367]	[a1,a2,a3,a4,a6]
Generators	[-107:21613:1]	Generators of the group modulo torsion
j	73877525106256274859/48189030400	j-invariant
L	5.9166955476237	L(r)(E,1)/r!
Ω	0.51320868006952	Real period
R	0.13724797434814	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	67760w2 76230ce2 42350a2 59290dv2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8470v2

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

---

Quadratic twists for elliptic curve 8470v2

-4	-3	5	-7	-11
67760w2	76230ce2	42350a2	59290dv2	8470a2

---

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