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	21840f	Isogeny class
Conductor	21840	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	1192464000000 = 210 · 32 · 56 · 72 · 132	Discriminant
Eigenvalues	2+ 3+ 5- 7+ -4 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-4480,104272]	[a1,a2,a3,a4,a6]
Generators	[-63:364:1] [-56:420:1]	Generators of the group modulo torsion
j	9713030100484/1164515625	j-invariant
L	6.700607740262	L(r)(E,1)/r!
Ω	0.83605288340237	Real period
R	0.66788117048625	Regulator
r	2	Rank of the group of rational points
S	0.99999999999998	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	10920i2 87360fz2 65520o2 109200cb2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840f2

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

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Quadratic twists for elliptic curve 21840f2

-4	8	-3	5
10920i2	87360fz2	65520o2	109200cb2

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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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