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	6440b	Isogeny class
Conductor	6440	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	2688	Modular degree for the optimal curve
Δ	-238473200 = -1 · 24 · 52 · 72 · 233	Discriminant
Eigenvalues	2+ -1 5+ 7+ -2 -5 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-936,11365]	[a1,a2,a3,a4,a6]
Generators	[-2:115:1] [6:77:1]	Generators of the group modulo torsion
j	-5674076449024/14904575	j-invariant
L	4.1763320743271	L(r)(E,1)/r!
Ω	1.7650391845375	Real period
R	0.098589219975822	Regulator
r	2	Rank of the group of rational points
S	0.99999999999988	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	12880c1 51520bb1 57960bt1 32200t1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6440b1

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
+	-1	+	+	-2	-5	-6	-6	-	-3	-3	0	-7	-6	-9	0	-4	-4	8	-13	-11	6	6	14	-2

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Quadratic twists for elliptic curve 6440b1

-4	8	-3	5	-7
12880c1	51520bb1	57960bt1	32200t1	45080n1

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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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