Cremona's table of elliptic curves

1825 = 5² · 73

Field	Data	Notes
Atkin-Lehner	5+ 73+	Signs for the Atkin-Lehner involutions
Class	1825a	Isogeny class
Conductor	1825	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	1140625 = 56 · 73	Discriminant
Eigenvalues	-1  0 5+ -2 -2  6 -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-30,-28]	[a1,a2,a3,a4,a6]
Generators	[-2:5:1]	Generators of the group modulo torsion
j	185193/73	j-invariant
L	1.7688723964573	L(r)(E,1)/r!
Ω	2.1156073592426	Real period
R	1.6722123684525	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	29200h1 116800b1 16425f1 73a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1825a1

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	+	-2	-2	6	-2	8	-4	2	-2	6	6	2	-6	-10	-6	-14	-8	0	+	-4	14	-6	10

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Quadratic twists for elliptic curve 1825a1

-4	8	-3	5	-7
29200h1	116800b1	16425f1	73a2	89425y1

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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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