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	21840s	Isogeny class
Conductor	21840	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	2631221013657600 = 211 · 32 · 52 · 7 · 138	Discriminant
Eigenvalues	2+ 3- 5- 7+  4 13-  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-76720,7772468]	[a1,a2,a3,a4,a6]
j	24385137179326562/1284775885575	j-invariant
L	3.59498437491	L(r)(E,1)/r!
Ω	0.44937304686375	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	10920n5 87360ea6 65520s6 109200o6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840s6

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
+	-	-	+	4	-	2	-4	0	6	8	-10	-6	4	8	6	-12	-2	12	8	10	-8	-4	-6	18

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Quadratic twists for elliptic curve 21840s6

-4	8	-3	5
10920n5	87360ea6	65520s6	109200o6

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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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