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	2048	Product of Tamagawa factors cp
Δ	97643750400000000 = 216 · 34 · 58 · 72 · 312	Discriminant
Eigenvalues	2- 3- 5- 7+  0 -6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-374955,87052977]	[a1,a2,a3,a4,a6]
Generators	[-426:13233:1]	Generators of the group modulo torsion
j	5829901703699110294321/97643750400000000	j-invariant
L	7.0467773301781	L(r)(E,1)/r!
Ω	0.33763684860973	Real period
R	0.16305373100924	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	52080bl2 19530k2 32550n2 45570bp2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6510ba2

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 6510ba2

-4	-3	5	-7
52080bl2	19530k2	32550n2	45570bp2

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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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