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	21840bp	Isogeny class
Conductor	21840	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	11793600000000 = 212 · 34 · 58 · 7 · 13	Discriminant
Eigenvalues	2- 3+ 5- 7- -4 13- -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-9640,-321488]	[a1,a2,a3,a4,a6]
Generators	[-46:150:1]	Generators of the group modulo torsion
j	24190225473961/2879296875	j-invariant
L	4.4148603700719	L(r)(E,1)/r!
Ω	0.48555949136633	Real period
R	1.1365395097233	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	1365f3 87360gc4 65520dd4 109200ff4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840bp4

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

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Quadratic twists for elliptic curve 21840bp4

-4	8	-3	5
1365f3	87360gc4	65520dd4	109200ff4

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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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