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	21840bi	Isogeny class
Conductor	21840	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-26864047042560 = -1 · 212 · 38 · 5 · 7 · 134	Discriminant
Eigenvalues	2- 3+ 5+ 7- -4 13+  6 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1576,251056]	[a1,a2,a3,a4,a6]
Generators	[10:486:1]	Generators of the group modulo torsion
j	-105756712489/6558605235	j-invariant
L	3.7687721567679	L(r)(E,1)/r!
Ω	0.55176136774943	Real period
R	1.7076096556652	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1365c4 87360hi3 65520ef3 109200ft3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840bi3

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	-8	4	-2	4	10	-2	-8	-8	6	-8	-10	12	8	6	-8	4	6	-2

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Quadratic twists for elliptic curve 21840bi3

-4	8	-3	5
1365c4	87360hi3	65520ef3	109200ft3

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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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