Cremona's table of elliptic curves

9840 = 2⁴ · 3 · 5 · 41

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 41-	Signs for the Atkin-Lehner involutions
Class	9840z	Isogeny class
Conductor	9840	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	36864	Modular degree for the optimal curve
Δ	61907927040000 = 228 · 32 · 54 · 41	Discriminant
Eigenvalues	2- 3- 5-  0 -4 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-78240,-8441100]	[a1,a2,a3,a4,a6]
Generators	[-165:60:1]	Generators of the group modulo torsion
j	12931706531187361/15114240000	j-invariant
L	5.4845362519249	L(r)(E,1)/r!
Ω	0.28547781215148	Real period
R	2.4014722066275	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	1230f1 39360br1 29520bh1 49200bt1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 9840z1

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

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Quadratic twists for elliptic curve 9840z1

-4	8	-3	5
1230f1	39360br1	29520bh1	49200bt1

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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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