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	21840o	Isogeny class
Conductor	21840	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	-35098574434560000 = -1 · 211 · 316 · 54 · 72 · 13	Discriminant
Eigenvalues	2+ 3- 5+ 7-  0 13+  2  0	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-27496,9173780]	[a1,a2,a3,a4,a6]
Generators	[-28:3150:1]	Generators of the group modulo torsion
j	-1122582097392338/17137975798125	j-invariant
L	6.177305645048	L(r)(E,1)/r!
Ω	0.31036111409359	Real period
R	0.62198771895611	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	10920a4 87360fn3 65520bj3 109200g3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840o3

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

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Quadratic twists for elliptic curve 21840o3

-4	8	-3	5
10920a4	87360fn3	65520bj3	109200g3

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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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