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	21840r	Isogeny class
Conductor	21840	Conductor
∏ cp	576	Product of Tamagawa factors cp
Δ	96589584000000 = 210 · 36 · 56 · 72 · 132	Discriminant
Eigenvalues	2+ 3- 5- 7+  0 13+ -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-11760,127908]	[a1,a2,a3,a4,a6]
Generators	[-54:780:1]	Generators of the group modulo torsion
j	175663952372164/94325765625	j-invariant
L	6.5957755794213	L(r)(E,1)/r!
Ω	0.52451748161523	Real period
R	0.34930387401589	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	10920f2 87360eg2 65520m2 109200s2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840r2

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	+	-2	4	-4	-2	0	-6	10	8	-12	-10	-4	2	4	-8	2	8	4	-14	2

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Quadratic twists for elliptic curve 21840r2

-4	8	-3	5
10920f2	87360eg2	65520m2	109200s2

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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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