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	1725k	Isogeny class
Conductor	1725	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	8625 = 3 · 53 · 23	Discriminant
Eigenvalues	1 3+ 5-  0  0  4  0 -2	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-5,0]	[a1,a2,a3,a4,a6]
Generators	[4:6:1]	Generators of the group modulo torsion
j	148877/69	j-invariant
L	3.0396872013791	L(r)(E,1)/r!
Ω	3.6917185231052	Real period
R	1.6467600020721	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	27600dd1 110400fd1 5175r1 1725r1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1725k1

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 1725k1

-4	8	-3	5	-7	-23
27600dd1	110400fd1	5175r1	1725r1	84525de1	39675s1

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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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