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	1610g	Isogeny class
Conductor	1610	Conductor
∏ cp	280	Product of Tamagawa factors cp
Δ	478174101507200 = 27 · 52 · 710 · 232	Discriminant
Eigenvalues	2- -2 5- 7- -2 -4 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-25120,-1116288]	[a1,a2,a3,a4,a6]
Generators	[-116:548:1]	Generators of the group modulo torsion
j	1753007192038126081/478174101507200	j-invariant
L	3.1616138593851	L(r)(E,1)/r!
Ω	0.38698913100038	Real period
R	0.11671106152303	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	12880w2 51520q2 14490o2 8050b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1610g2

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

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Quadratic twists for elliptic curve 1610g2

-4	8	-3	5	-7	-23
12880w2	51520q2	14490o2	8050b2	11270n2	37030n2

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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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