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	1725r	Isogeny class
Conductor	1725	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-9298828125 = -1 · 32 · 59 · 232	Discriminant
Eigenvalues	-1 3- 5-  0  0 -4  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,487,2142]	[a1,a2,a3,a4,a6]
Generators	[13:97:1]	Generators of the group modulo torsion
j	6539203/4761	j-invariant
L	2.2121943395081	L(r)(E,1)/r!
Ω	0.82549335714583	Real period
R	1.3399225568312	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	27600ca2 110400bt2 5175v2 1725k2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1725r2

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

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Quadratic twists for elliptic curve 1725r2

-4	8	-3	5	-7	-23
27600ca2	110400bt2	5175v2	1725k2	84525z2	39675bo2

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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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