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	6510o	Isogeny class
Conductor	6510	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-121212131250000 = -1 · 24 · 3 · 58 · 7 · 314	Discriminant
Eigenvalues	2- 3+ 5+ 7+ -4  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-10721,676079]	[a1,a2,a3,a4,a6]
Generators	[29:610:1]	Generators of the group modulo torsion
j	-136280002216368529/121212131250000	j-invariant
L	4.5867305299856	L(r)(E,1)/r!
Ω	0.53823931297803	Real period
R	1.0652163497236	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	52080bs3 19530ba4 32550bd3 45570dg3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6510o4

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
-	+	+	+	-4	2	-2	4	0	2	-	6	6	-8	-12	2	0	-6	-4	-8	6	4	-4	6	-6

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Quadratic twists for elliptic curve 6510o4

-4	-3	5	-7
52080bs3	19530ba4	32550bd3	45570dg3

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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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