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	8	Product of Tamagawa factors cp
Δ	-83265625 = -1 · 56 · 732	Discriminant
Eigenvalues	-1  0 5+ -2 -2  6 -2  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,95,-278]	[a1,a2,a3,a4,a6]
Generators	[4:10:1]	Generators of the group modulo torsion
j	6128487/5329	j-invariant
L	1.7688723964573	L(r)(E,1)/r!
Ω	1.0578036796213	Real period
R	0.83610618422625	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	29200h2 116800b2 16425f2 73a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1825a2

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 1825a2

-4	8	-3	5	-7
29200h2	116800b2	16425f2	73a1	89425y2

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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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