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	21840bl	Isogeny class
Conductor	21840	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	68796000000 = 28 · 33 · 56 · 72 · 13	Discriminant
Eigenvalues	2- 3+ 5- 7+  0 13-  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1580,-20100]	[a1,a2,a3,a4,a6]
j	1705021456336/268734375	j-invariant
L	2.2957549140628	L(r)(E,1)/r!
Ω	0.76525163802093	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	5460g2 87360fv2 65520cr2 109200ga2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840bl2

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	4	0	6	-8	8	-6	10	12	0	-6	2	-8	12	2	4	-12	6	14

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Quadratic twists for elliptic curve 21840bl2

-4	8	-3	5
5460g2	87360fv2	65520cr2	109200ga2

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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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