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	21840d	Isogeny class
Conductor	21840	Conductor
∏ cp	256	Product of Tamagawa factors cp
Δ	-316125084213120000 = -1 · 210 · 3 · 54 · 78 · 134	Discriminant
Eigenvalues	2+ 3+ 5+ 7-  0 13- -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-95256,-29290944]	[a1,a2,a3,a4,a6]
Generators	[500:6916:1]	Generators of the group modulo torsion
j	-93348068573646436/308715902551875	j-invariant
L	3.8463092013279	L(r)(E,1)/r!
Ω	0.12506694915916	Real period
R	1.9221251233775	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	10920p4 87360hb3 65520bp3 109200bm3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840d3

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

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Quadratic twists for elliptic curve 21840d3

-4	8	-3	5
10920p4	87360hb3	65520bp3	109200bm3

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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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