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	21840bd	Isogeny class
Conductor	21840	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	5.5800568715674E+20	Discriminant
Eigenvalues	2- 3+ 5+ 7+  0 13- -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2504936,1019105136]	[a1,a2,a3,a4,a6]
Generators	[-742:49686:1]	Generators of the group modulo torsion
j	424378956393532177129/136231857216000000	j-invariant
L	3.644933026092	L(r)(E,1)/r!
Ω	0.15143543721342	Real period
R	2.0057684279864	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	2730n6 87360gr6 65520du6 109200fy6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840bd6

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

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Quadratic twists for elliptic curve 21840bd6

-4	8	-3	5
2730n6	87360gr6	65520du6	109200fy6

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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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