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	1725d	Isogeny class
Conductor	1725	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	421142578125 = 3 · 514 · 23	Discriminant
Eigenvalues	1 3+ 5+ -4 -4  2 -6  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-9525,352500]	[a1,a2,a3,a4,a6]
j	6117442271569/26953125	j-invariant
L	0.94852751040587	L(r)(E,1)/r!
Ω	0.94852751040587	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	27600cp3 110400ek3 5175e3 345d4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1725d4

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	+	+	-4	-4	2	-6	8	-	6	8	-6	-6	8	8	-2	-4	-10	-8	0	6	-4	12	6	14

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Quadratic twists for elliptic curve 1725d4

-4	8	-3	5	-7	-23
27600cp3	110400ek3	5175e3	345d4	84525ck3	39675h3

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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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