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	1725q	Isogeny class
Conductor	1725	Conductor
∏ cp	54	Product of Tamagawa factors cp
deg	1080	Modular degree for the optimal curve
Δ	-6507691875 = -1 · 39 · 54 · 232	Discriminant
Eigenvalues	0 3- 5- -1 -6  5  0  5	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,467,244]	[a1,a2,a3,a4,a6]
Generators	[2:34:1]	Generators of the group modulo torsion
j	17983078400/10412307	j-invariant
L	2.8002614113552	L(r)(E,1)/r!
Ω	0.80019631357325	Real period
R	0.58324467047566	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	27600cd1 110400bw1 5175u1 1725c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1725q1

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	-	-	-1	-6	5	0	5	+	0	-7	-10	-12	-1	-6	-12	-6	5	-13	12	2	8	6	6	11

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Quadratic twists for elliptic curve 1725q1

-4	8	-3	5	-7	-23
27600cd1	110400bw1	5175u1	1725c1	84525x1	39675bj1

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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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