Cremona's table of elliptic curves

107584 = 2⁶ · 41²

Field	Data	Notes
Atkin-Lehner	2+ 41+	Signs for the Atkin-Lehner involutions
Class	107584c	Isogeny class
Conductor	107584	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	289075625984 = 222 · 413	Discriminant
Eigenvalues	2+  2 -2  2 -6  4  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-223969,-40722591]	[a1,a2,a3,a4,a6]
Generators	[-4049250378264:-8841753955:14832537993]	Generators of the group modulo torsion
j	68769820673/16	j-invariant
L	7.9721922098566	L(r)(E,1)/r!
Ω	0.21945850755542	Real period
R	18.163324622786	Regulator
r	1	Rank of the group of rational points
S	0.99999999773387	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	107584o2 3362c2 107584e2	Quadratic twists by: -4 8 41

Hecke Eigenvalues for elliptic curve 107584c2

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

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Quadratic twists for elliptic curve 107584c2

-4	8	41
107584o2	3362c2	107584e2

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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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