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	8610t	Isogeny class
Conductor	8610	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	1186819620 = 22 · 3 · 5 · 7 · 414	Discriminant
Eigenvalues	2- 3- 5- 7- -4  6  6  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2275,-41923]	[a1,a2,a3,a4,a6]
j	1302206462247601/1186819620	j-invariant
L	5.5305326377936	L(r)(E,1)/r!
Ω	0.6913165797242	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	68880bq4 25830m4 43050c4 60270r4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8610t3

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

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Quadratic twists for elliptic curve 8610t3

-4	-3	5	-7
68880bq4	25830m4	43050c4	60270r4

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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