Cremona's table of elliptic curves

6510 = 2 · 3 · 5 · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 7+ 31-	Signs for the Atkin-Lehner involutions
Class	6510ba	Isogeny class
Conductor	6510	Conductor
∏ cp	1024	Product of Tamagawa factors cp
Δ	6786327834720000 = 28 · 38 · 54 · 7 · 314	Discriminant
Eigenvalues	2- 3- 5- 7+  0 -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-5974955,5620972977]	[a1,a2,a3,a4,a6]
Generators	[3574:-174767:1]	Generators of the group modulo torsion
j	23589983275298076108694321/6786327834720000	j-invariant
L	7.0467773301781	L(r)(E,1)/r!
Ω	0.33763684860973	Real period
R	0.32610746201847	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	52080bl4 19530k3 32550n4 45570bp4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6510ba3

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	-6	-2	-4	-4	-2	-	-10	2	0	-8	-2	-4	-6	12	-16	14	-4	12	6	10

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Quadratic twists for elliptic curve 6510ba3

-4	-3	5	-7
52080bl4	19530k3	32550n4	45570bp4

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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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