Cremona's table of elliptic curves

5525 = 5² · 13 · 17

Field	Data	Notes
Atkin-Lehner	5+ 13- 17+	Signs for the Atkin-Lehner involutions
Class	5525d	Isogeny class
Conductor	5525	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	9920828125 = 56 · 133 · 172	Discriminant
Eigenvalues	1  0 5+  2  6 13- 17+  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-292942,61100091]	[a1,a2,a3,a4,a6]
j	177930109857804849/634933	j-invariant
L	2.5826920124006	L(r)(E,1)/r!
Ω	0.86089733746687	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	88400bi2 49725s2 221a2 71825g2	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5525d2

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

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Quadratic twists for elliptic curve 5525d2

-4	-3	5	13	17
88400bi2	49725s2	221a2	71825g2	93925f2

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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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