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	1725f	Isogeny class
Conductor	1725	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	24796875 = 3 · 56 · 232	Discriminant
Eigenvalues	-1 3+ 5+  2  4  6 -4  2	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-388,-3094]	[a1,a2,a3,a4,a6]
j	413493625/1587	j-invariant
L	1.0759350304954	L(r)(E,1)/r!
Ω	1.0759350304954	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	27600cn2 110400dx2 5175b2 69a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1725f2

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	4	6	-4	2	-	2	4	-2	2	-10	0	12	-12	-6	10	8	14	10	-12	-16	10

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Quadratic twists for elliptic curve 1725f2

-4	8	-3	5	-7	-23
27600cn2	110400dx2	5175b2	69a2	84525co2	39675j2

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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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