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	5525c	Isogeny class
Conductor	5525	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	19200	Modular degree for the optimal curve
Δ	10791015625 = 511 · 13 · 17	Discriminant
Eigenvalues	1  0 5+  2 -4 13- 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-359692,-82941909]	[a1,a2,a3,a4,a6]
j	329379602649536529/690625	j-invariant
L	1.5595768875727	L(r)(E,1)/r!
Ω	0.19494711094659	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	16	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	88400bh1 49725r1 1105a1 71825f1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 5525c1

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	-4	-	+	-2	-4	-6	8	-2	10	6	0	6	10	10	8	-8	-10	10	-16	18	14

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Quadratic twists for elliptic curve 5525c1

-4	-3	5	13	17
88400bh1	49725r1	1105a1	71825f1	93925e1

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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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