Cremona's table of elliptic curves

6440 = 2³ · 5 · 7 · 23

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 23-	Signs for the Atkin-Lehner involutions
Class	6440f	Isogeny class
Conductor	6440	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	12288	Modular degree for the optimal curve
Δ	3155600000000 = 210 · 58 · 73 · 23	Discriminant
Eigenvalues	2- -2 5+ 7+ -6  4  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4296,-68096]	[a1,a2,a3,a4,a6]
Generators	[72:32:1]	Generators of the group modulo torsion
j	8564808605476/3081640625	j-invariant
L	2.204665412865	L(r)(E,1)/r!
Ω	0.60732915314836	Real period
R	3.630099759638	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	12880d1 51520bc1 57960u1 32200e1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6440f1

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
-	-2	+	+	-6	4	2	-4	-	6	-4	4	-2	-6	0	8	6	6	10	0	-14	16	-4	-2	-2

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Quadratic twists for elliptic curve 6440f1

-4	8	-3	5	-7
12880d1	51520bc1	57960u1	32200e1	45080bi1

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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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