Cremona's table of elliptic curves

725 = 5² · 29

Field	Data	Notes
Atkin-Lehner	5+ 29+	Signs for the Atkin-Lehner involutions
Class	725a	Isogeny class
Conductor	725	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-328515625 = -1 · 58 · 292	Discriminant
Eigenvalues	1  0 5+  2 -6 -2  2 -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,58,841]	[a1,a2,a3,a4,a6]
Generators	[0:29:1]	Generators of the group modulo torsion
j	1367631/21025	j-invariant
L	2.6227061923179	L(r)(E,1)/r!
Ω	1.2726757762609	Real period
R	1.0303905524246	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	11600q2 46400k2 6525h2 145a2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 725a2

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	-6	-2	2	-2	-2	+	2	-10	2	-8	12	6	-8	-6	-2	-12	6	-10	14	18	-2

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Quadratic twists for elliptic curve 725a2

-4	8	-3	5	-7	-11	13	29
11600q2	46400k2	6525h2	145a2	35525d2	87725o2	122525c2	21025a2

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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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