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	21840cb	Isogeny class
Conductor	21840	Conductor
∏ cp	160	Product of Tamagawa factors cp
deg	2764800	Modular degree for the optimal curve
Δ	7.2747998585605E+22	Discriminant
Eigenvalues	2- 3- 5+ 7- -4 13- -6  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-11520696,-7628493996]	[a1,a2,a3,a4,a6]
Generators	[-2970:19968:1]	Generators of the group modulo torsion
j	41285728533151645510969/17760741842188800000	j-invariant
L	5.7395824824246	L(r)(E,1)/r!
Ω	0.085201616244922	Real period
R	1.6841178417101	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	2730c1 87360fl1 65520en1 109200da1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 21840cb1

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

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Quadratic twists for elliptic curve 21840cb1

-4	8	-3	5
2730c1	87360fl1	65520en1	109200da1

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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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