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	21840a	Isogeny class
Conductor	21840	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	382112640000 = 210 · 38 · 54 · 7 · 13	Discriminant
Eigenvalues	2+ 3+ 5+ 7+  4 13+ -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2616,-41184]	[a1,a2,a3,a4,a6]
Generators	[61:150:1]	Generators of the group modulo torsion
j	1934207124196/373156875	j-invariant
L	3.8949076962958	L(r)(E,1)/r!
Ω	0.6764918123092	Real period
R	2.8787544988908	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	10920h4 87360ha3 65520be3 109200ca3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840a3

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	0	-4	-2	4	2	6	-8	0	6	0	-2	4	-16	-10	16	12	14	-18

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Quadratic twists for elliptic curve 21840a3

-4	8	-3	5
10920h4	87360ha3	65520be3	109200ca3

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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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