Cremona's table of elliptic curves

21840 = 2⁴ · 3 · 5 · 7 · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 7+ 13+	Signs for the Atkin-Lehner involutions
Class	21840k	Isogeny class
Conductor	21840	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	-1.0636393218063E+20	Discriminant
Eigenvalues	2+ 3- 5+ 7+  0 13+ -6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1526936,-880074636]	[a1,a2,a3,a4,a6]
j	-192245661431796830258/51935513760073125	j-invariant
L	1.0714208733614	L(r)(E,1)/r!
Ω	0.06696380458509	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	10920b4 87360fc3 65520bb3 109200t3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840k3

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	+	-6	-8	-4	6	0	-6	-6	4	-8	2	-8	-2	12	0	-2	-8	4	18	-2

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Quadratic twists for elliptic curve 21840k3

-4	8	-3	5
10920b4	87360fc3	65520bb3	109200t3

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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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