Cremona's table of elliptic curves

40992 = 2⁵ · 3 · 7 · 61

Field	Data	Notes
Atkin-Lehner	2+ 3- 7+ 61-	Signs for the Atkin-Lehner involutions
Class	40992i	Isogeny class
Conductor	40992	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	13824	Modular degree for the optimal curve
Δ	-141668352 = -1 · 212 · 34 · 7 · 61	Discriminant
Eigenvalues	2+ 3-  0 7+  2  4 -3 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-413,3147]	[a1,a2,a3,a4,a6]
Generators	[13:12:1]	Generators of the group modulo torsion
j	-1906624000/34587	j-invariant
L	7.0444601429099	L(r)(E,1)/r!
Ω	1.8400329171084	Real period
R	0.47855530717773	Regulator
r	1	Rank of the group of rational points
S	0.99999999999976	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	40992o1 81984a1 122976be1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 40992i1

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	+	2	4	-3	-6	0	-2	-11	6	6	-4	8	-4	-3	-	12	-6	10	12	6	10	12

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Quadratic twists for elliptic curve 40992i1

-4	8	-3
40992o1	81984a1	122976be1

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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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