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	9840c	Isogeny class
Conductor	9840	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	2560	Modular degree for the optimal curve
Δ	9446400 = 210 · 32 · 52 · 41	Discriminant
Eigenvalues	2+ 3+ 5+ -2 -6 -2 -4 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-136,640]	[a1,a2,a3,a4,a6]
Generators	[-10:30:1] [-2:30:1]	Generators of the group modulo torsion
j	273671716/9225	j-invariant
L	4.7170287730991	L(r)(E,1)/r!
Ω	2.2889035891909	Real period
R	0.51520614448068	Regulator
r	2	Rank of the group of rational points
S	0.9999999999998	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	4920i1 39360df1 29520r1 49200bf1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 9840c1

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
+	+	+	-2	-6	-2	-4	-2	0	4	-8	-2	-	4	-6	-6	-12	-6	-12	-12	-14	-16	12	-10	-12

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Quadratic twists for elliptic curve 9840c1

-4	8	-3	5
4920i1	39360df1	29520r1	49200bf1

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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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