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	8610m	Isogeny class
Conductor	8610	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	185330250000 = 24 · 32 · 56 · 72 · 412	Discriminant
Eigenvalues	2- 3+ 5- 7+ -4  6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-143500,-20982883]	[a1,a2,a3,a4,a6]
j	326798161405652664001/185330250000	j-invariant
L	2.9435256489767	L(r)(E,1)/r!
Ω	0.24529380408139	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	68880cx2 25830i2 43050x2 60270bk2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 8610m2

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

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Quadratic twists for elliptic curve 8610m2

-4	-3	5	-7
68880cx2	25830i2	43050x2	60270bk2

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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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