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	5525h	Isogeny class
Conductor	5525	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	4800	Modular degree for the optimal curve
Δ	1467578125 = 58 · 13 · 172	Discriminant
Eigenvalues	0  3 5-  0  0 13+ 17+ -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-1000,12031]	[a1,a2,a3,a4,a6]
j	283115520/3757	j-invariant
L	3.0345375119726	L(r)(E,1)/r!
Ω	1.5172687559863	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	88400bw1 49725w1 5525g1 71825n1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5525h1

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
0	3	-	0	0	+	+	-6	9	3	-2	-4	10	5	6	7	10	13	-12	0	-16	5	-10	18	8

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Quadratic twists for elliptic curve 5525h1

-4	-3	5	13	17
88400bw1	49725w1	5525g1	71825n1	93925p1

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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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