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	5525i	Isogeny class
Conductor	5525	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	19200	Modular degree for the optimal curve
Δ	424130078125 = 58 · 13 · 174	Discriminant
Eigenvalues	2 -3 5- -2  2 13+ 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-5875,-170469]	[a1,a2,a3,a4,a6]
Generators	[-350:421:8]	Generators of the group modulo torsion
j	57409966080/1085773	j-invariant
L	4.39749459686	L(r)(E,1)/r!
Ω	0.54594188403665	Real period
R	0.67123973043084	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	88400bx1 49725v1 5525f1 71825s1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5525i1

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
2	-3	-	-2	2	+	-	4	-5	9	2	-4	-8	9	0	3	4	7	-2	-8	-2	-5	4	-6	-8

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Quadratic twists for elliptic curve 5525i1

-4	-3	5	13	17
88400bx1	49725v1	5525f1	71825s1	93925r1

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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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