Cremona's table of elliptic curves

6525 = 3² · 5² · 29

Field	Data	Notes
Atkin-Lehner	3- 5+ 29+	Signs for the Atkin-Lehner involutions
Class	6525c	Isogeny class
Conductor	6525	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2688	Modular degree for the optimal curve
Δ	-33520641075 = -1 · 313 · 52 · 292	Discriminant
Eigenvalues	0 3- 5+ -1  2  3  4  1	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-1380,-21609]	[a1,a2,a3,a4,a6]
j	-15947530240/1839267	j-invariant
L	1.5565122927063	L(r)(E,1)/r!
Ω	0.38912807317656	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	104400ds1 2175g1 6525i1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 6525c1

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	3	4	1	0	+	-1	-6	8	1	6	-2	0	-3	-5	6	6	-12	6	4	1

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Quadratic twists for elliptic curve 6525c1

-4	-3	5
104400ds1	2175g1	6525i1

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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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