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	9840f	Isogeny class
Conductor	9840	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	2343799203840 = 211 · 34 · 5 · 414	Discriminant
Eigenvalues	2+ 3+ 5-  4  0 -2 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-17840,920160]	[a1,a2,a3,a4,a6]
Generators	[746:1939:8]	Generators of the group modulo torsion
j	306621535079522/1144433205	j-invariant
L	4.5113623484708	L(r)(E,1)/r!
Ω	0.82172444202273	Real period
R	5.4901158073938	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	4920j3 39360ct4 29520j4 49200bi4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 9840f3

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

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Quadratic twists for elliptic curve 9840f3

-4	8	-3	5
4920j3	39360ct4	29520j4	49200bi4

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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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