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
deg	6912	Modular degree for the optimal curve
Δ	-69209437500 = -1 · 22 · 36 · 56 · 72 · 31	Discriminant
Eigenvalues	2+ 3- 5- 7-  0 -4 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-113,12656]	[a1,a2,a3,a4,a6]
Generators	[-18:103:1]	Generators of the group modulo torsion
j	-157551496201/69209437500	j-invariant
L	3.8080620519223	L(r)(E,1)/r!
Ω	0.88985866501915	Real period
R	1.0698502474661	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	6	Number of elements in the torsion subgroup
Twists	52080bg1 19530bx1 32550br1 45570c1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6510k1

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 6510k1

-4	-3	5	-7
52080bg1	19530bx1	32550br1	45570c1

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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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