Cremona's table of elliptic curves

107822 = 2 · 11 · 13² · 29

Field	Data	Notes
Atkin-Lehner	2- 11- 13- 29-	Signs for the Atkin-Lehner involutions
Class	107822r	Isogeny class
Conductor	107822	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	197184	Modular degree for the optimal curve
Δ	-6765670599974 = -1 · 2 · 11 · 139 · 29	Discriminant
Eigenvalues	2-  0 -1 -3 11- 13- -3 -3	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-10848,455225]	[a1,a2,a3,a4,a6]
Generators	[8790:285605:8]	Generators of the group modulo torsion
j	-13312053/638	j-invariant
L	6.7434916126644	L(r)(E,1)/r!
Ω	0.74100867245776	Real period
R	4.550210990847	Regulator
r	1	Rank of the group of rational points
S	1.0000000001785	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	107822g1	Quadratic twists by: 13

Hecke Eigenvalues for elliptic curve 107822r1

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	-1	-3	-	-	-3	-3	3	-	-1	10	-2	2	-12	-6	-4	6	4	4	-2	13	4	-7	13

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Quadratic twists for elliptic curve 107822r1

13
107822g1

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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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