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	6510k	Isogeny class
Conductor	6510	Conductor
∏ cp	144	Product of Tamagawa factors cp
Δ	-50470291569600 = -1 · 26 · 32 · 52 · 76 · 313	Discriminant
Eigenvalues	2+ 3- 5- 7-  0 -4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,1012,-341494]	[a1,a2,a3,a4,a6]
Generators	[72:289:1]	Generators of the group modulo torsion
j	114784170265799/50470291569600	j-invariant
L	3.8080620519223	L(r)(E,1)/r!
Ω	0.29661955500638	Real period
R	0.35661674915536	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	52080bg3 19530bx3 32550br3 45570c3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6510k3

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	-4	-6	-4	0	0	-	2	6	2	12	6	-12	-10	-4	0	2	-10	-12	-12	2

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Quadratic twists for elliptic curve 6510k3

-4	-3	5	-7
52080bg3	19530bx3	32550br3	45570c3

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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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