Cremona's table of elliptic curves

8610 = 2 · 3 · 5 · 7 · 41

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 7+ 41-	Signs for the Atkin-Lehner involutions
Class	8610s	Isogeny class
Conductor	8610	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	45392075103226320 = 24 · 324 · 5 · 72 · 41	Discriminant
Eigenvalues	2- 3- 5- 7+  0 -6 -2  0	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-868245,-311298543]	[a1,a2,a3,a4,a6]
Generators	[-528:345:1]	Generators of the group modulo torsion
j	72385339621521918736081/45392075103226320	j-invariant
L	7.6366828485222	L(r)(E,1)/r!
Ω	0.15640669037979	Real period
R	1.0172043085746	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	68880bx4 25830h4 43050g4 60270q4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8610s3

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

---

Quadratic twists for elliptic curve 8610s3

-4	-3	5	-7
68880bx4	25830h4	43050g4	60270q4

---

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