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	5525b	Isogeny class
Conductor	5525	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	2400	Modular degree for the optimal curve
Δ	36689453125 = 510 · 13 · 172	Discriminant
Eigenvalues	0  1 5+  2  2 13+ 17-  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-833,619]	[a1,a2,a3,a4,a6]
j	6553600/3757	j-invariant
L	1.9783869193701	L(r)(E,1)/r!
Ω	0.98919345968505	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	88400y1 49725e1 5525j1 71825k1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5525b1

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	1	+	2	2	+	-	2	7	-1	0	0	0	-1	-12	5	8	9	0	12	-12	-3	-6	-2	6

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Quadratic twists for elliptic curve 5525b1

-4	-3	5	13	17
88400y1	49725e1	5525j1	71825k1	93925b1

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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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