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	8	Product of Tamagawa factors cp
Δ	156632893013671875 = 320 · 59 · 23	Discriminant
Eigenvalues	-1 3+ 5+ -4  4 -6  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-414088,-100951594]	[a1,a2,a3,a4,a6]
j	502552788401502649/10024505152875	j-invariant
L	0.37686243575434	L(r)(E,1)/r!
Ω	0.18843121787717	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	27600cq3 110400el3 5175c4 345c3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1725g3

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 1725g3

-4	8	-3	5	-7	-23
27600cq3	110400el3	5175c4	345c3	84525cn3	39675k3

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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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