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	6510p	Isogeny class
Conductor	6510	Conductor
∏ cp	40	Product of Tamagawa factors cp
Δ	311675678465185440 = 25 · 316 · 5 · 72 · 314	Discriminant
Eigenvalues	2- 3+ 5- 7+  0 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-173170,6846047]	[a1,a2,a3,a4,a6]
Generators	[-195:5863:1]	Generators of the group modulo torsion
j	574303998127522229281/311675678465185440	j-invariant
L	5.322913948378	L(r)(E,1)/r!
Ω	0.26687200840256	Real period
R	1.9945568590127	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	52080cg3 19530g4 32550w3 45570cv3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6510p3

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	-2	6	-4	-4	-6	+	-10	-6	4	-8	6	4	2	-4	0	-2	-8	4	10	2

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Quadratic twists for elliptic curve 6510p3

-4	-3	5	-7
52080cg3	19530g4	32550w3	45570cv3

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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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