Cremona's table of elliptic curves

1610 = 2 · 5 · 7 · 23

Field	Data	Notes
Atkin-Lehner	2- 5- 7+ 23+	Signs for the Atkin-Lehner involutions
Class	1610f	Isogeny class
Conductor	1610	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	2592100 = 22 · 52 · 72 · 232	Discriminant
Eigenvalues	2-  0 5- 7+ -4 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-537,-4651]	[a1,a2,a3,a4,a6]
Generators	[59:378:1]	Generators of the group modulo torsion
j	17095749786081/2592100	j-invariant
L	3.9000243575857	L(r)(E,1)/r!
Ω	0.99191198082227	Real period
R	3.9318250338631	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	12880y2 51520c2 14490k2 8050l2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1610f2

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

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Quadratic twists for elliptic curve 1610f2

-4	8	-3	5	-7	-23
12880y2	51520c2	14490k2	8050l2	11270k2	37030o2

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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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