Cremona's table of elliptic curves

123786 = 2 · 3² · 13 · 23²

Field	Data	Notes
Atkin-Lehner	2- 3- 13- 23-	Signs for the Atkin-Lehner involutions
Class	123786bk	Isogeny class
Conductor	123786	Conductor
∏ cp	384	Product of Tamagawa factors cp
deg	1179648	Modular degree for the optimal curve
Δ	-84048392665755648 = -1 · 212 · 310 · 134 · 233	Discriminant
Eigenvalues	2- 3-  0 -4 -4 13-  4  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,83425,10397319]	[a1,a2,a3,a4,a6]
Generators	[167:-5466:1]	Generators of the group modulo torsion
j	7239460488625/9475854336	j-invariant
L	7.928750868223	L(r)(E,1)/r!
Ω	0.22971881931765	Real period
R	0.35953151090506	Regulator
r	1	Rank of the group of rational points
S	1.0000000082905	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	41262c1 123786bj1	Quadratic twists by: -3 -23

Hecke Eigenvalues for elliptic curve 123786bk1

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	-4	-4	-	4	0	-	-2	0	4	-10	-8	8	0	-4	4	8	0	-10	4	4	12	8

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Quadratic twists for elliptic curve 123786bk1

-3	-23
41262c1	123786bj1

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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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