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	21840j	Isogeny class
Conductor	21840	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	29929002055680 = 211 · 3 · 5 · 78 · 132	Discriminant
Eigenvalues	2+ 3+ 5- 7-  4 13-  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-108960,13877472]	[a1,a2,a3,a4,a6]
j	69855246474511682/14613770535	j-invariant
L	2.5728777918888	L(r)(E,1)/r!
Ω	0.64321944797221	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	10920t5 87360gd6 65520ba6 109200bn6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840j6

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

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Quadratic twists for elliptic curve 21840j6

-4	8	-3	5
10920t5	87360gd6	65520ba6	109200bn6

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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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