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	1725g	Isogeny class
Conductor	1725	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	21320343017578125 = 35 · 518 · 23	Discriminant
Eigenvalues	-1 3+ 5+ -4  4 -6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-753338,251258906]	[a1,a2,a3,a4,a6]
j	3026030815665395929/1364501953125	j-invariant
L	0.37686243575434	L(r)(E,1)/r!
Ω	0.37686243575434	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	27600cq4 110400el4 5175c3 345c4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1725g4

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	-6	2	-4	-	-10	-8	-2	2	8	0	6	0	6	-8	-4	-10	16	12	-10	10

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Quadratic twists for elliptic curve 1725g4

-4	8	-3	5	-7	-23
27600cq4	110400el4	5175c3	345c4	84525cn4	39675k4

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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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