Cremona's table of elliptic curves

6390 = 2 · 3² · 5 · 71

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 71+	Signs for the Atkin-Lehner involutions
Class	6390k	Isogeny class
Conductor	6390	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8160	Modular degree for the optimal curve
Δ	169603891200 = 217 · 36 · 52 · 71	Discriminant
Eigenvalues	2+ 3- 5- -1  2 -1  4 -1	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-3744,-84992]	[a1,a2,a3,a4,a6]
Generators	[-33:59:1]	Generators of the group modulo torsion
j	7962857630209/232652800	j-invariant
L	3.2130033371757	L(r)(E,1)/r!
Ω	0.61141484092231	Real period
R	2.6275150046481	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	51120bn1 710b1 31950by1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 6390k1

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	-1	4	-1	5	-4	-9	-8	-8	-7	-13	6	8	10	4	+	-7	6	16	-17	18

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Quadratic twists for elliptic curve 6390k1

-4	-3	5
51120bn1	710b1	31950by1

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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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