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	1725p	Isogeny class
Conductor	1725	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	2304	Modular degree for the optimal curve
Δ	-76994296875 = -1 · 34 · 57 · 233	Discriminant
Eigenvalues	-2 3- 5+ -3  2  2 -5 -2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,742,-10606]	[a1,a2,a3,a4,a6]
Generators	[88:-863:1]	Generators of the group modulo torsion
j	2887553024/4927635	j-invariant
L	1.7243846017332	L(r)(E,1)/r!
Ω	0.5715387360114	Real period
R	0.12571214141488	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	27600bk1 110400bj1 5175g1 345e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1725p1

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
-2	-	+	-3	2	2	-5	-2	-	-5	3	7	-11	8	-8	-5	-1	-8	9	1	-10	0	-15	0	10

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Quadratic twists for elliptic curve 1725p1

-4	8	-3	5	-7	-23
27600bk1	110400bj1	5175g1	345e1	84525t1	39675bh1

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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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