Cremona's table of elliptic curves

1725 = 3 · 5² · 23

Field	Data	Notes
Atkin-Lehner	3+ 5+ 23+	Signs for the Atkin-Lehner involutions
Class	1725a	Isogeny class
Conductor	1725	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	384	Modular degree for the optimal curve
Δ	-16171875 = -1 · 32 · 57 · 23	Discriminant
Eigenvalues	0 3+ 5+  3 -4  0  3 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,-33,218]	[a1,a2,a3,a4,a6]
Generators	[12:37:1]	Generators of the group modulo torsion
j	-262144/1035	j-invariant
L	2.2184719410642	L(r)(E,1)/r!
Ω	1.9220175446073	Real period
R	0.14428015676084	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	27600db1 110400dd1 5175j1 345b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1725a1

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	+	+	3	-4	0	3	-8	+	9	-5	9	7	-4	2	-13	-3	-14	-13	-13	4	0	1	-8	-10

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Quadratic twists for elliptic curve 1725a1

-4	8	-3	5	-7	-23
27600db1	110400dd1	5175j1	345b1	84525bt1	39675d1

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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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