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	1725j	Isogeny class
Conductor	1725	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	14400	Modular degree for the optimal curve
Δ	31182690234375 = 38 · 58 · 233	Discriminant
Eigenvalues	-1 3+ 5-  3  5  1  8  1	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-381513,90541656]	[a1,a2,a3,a4,a6]
j	15721420060947505/79827687	j-invariant
L	1.1678036193431	L(r)(E,1)/r!
Ω	0.58390180967157	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	27600di1 110400ex1 5175x1 1725o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1725j1

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	+	-	3	5	1	8	1	+	-5	-6	8	-5	13	2	-10	-4	4	0	10	13	-9	-15	-6	2

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Quadratic twists for elliptic curve 1725j1

-4	8	-3	5	-7	-23
27600di1	110400ex1	5175x1	1725o1	84525da1	39675v1

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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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