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
deg	4480	Modular degree for the optimal curve
Δ	3958384640000 = 214 · 54 · 75 · 23	Discriminant
Eigenvalues	2- -2 5- 7- -2 -4 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-9120,320512]	[a1,a2,a3,a4,a6]
Generators	[-96:608:1]	Generators of the group modulo torsion
j	83890194895342081/3958384640000	j-invariant
L	3.1616138593851	L(r)(E,1)/r!
Ω	0.77397826200076	Real period
R	0.058355530761517	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	12880w1 51520q1 14490o1 8050b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1610g1

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 1610g1

-4	8	-3	5	-7	-23
12880w1	51520q1	14490o1	8050b1	11270n1	37030n1

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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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