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	6525f	Isogeny class
Conductor	6525	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	14864765625 = 38 · 57 · 29	Discriminant
Eigenvalues	-1 3- 5+  4  0 -6  2  8	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-1566005,754680372]	[a1,a2,a3,a4,a6]
j	37286818682653441/1305	j-invariant
L	1.3310099551354	L(r)(E,1)/r!
Ω	0.66550497756771	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	104400ef4 2175b3 1305c3	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 6525f3

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	-	+	4	0	-6	2	8	-4	+	4	-6	-2	4	0	6	12	6	8	-16	6	12	-16	-2	14

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Quadratic twists for elliptic curve 6525f3

-4	-3	5
104400ef4	2175b3	1305c3

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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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