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	1725u	Isogeny class
Conductor	1725	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	240	Modular degree for the optimal curve
Δ	-1785375 = -1 · 33 · 53 · 232	Discriminant
Eigenvalues	1 3- 5-  2  0  4  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-36,-107]	[a1,a2,a3,a4,a6]
j	-39651821/14283	j-invariant
L	2.8813622202588	L(r)(E,1)/r!
Ω	0.96045407341959	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	27600bv1 110400cj1 5175s1 1725i1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1725u1

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
1	-	-	2	0	4	2	-4	-	10	4	2	-10	2	8	10	6	-6	-10	10	-8	16	0	4	-2

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Quadratic twists for elliptic curve 1725u1

-4	8	-3	5	-7	-23
27600bv1	110400cj1	5175s1	1725i1	84525bg1	39675bn1

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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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