Cremona's table of elliptic curves

106 = 2 · 53

Field	Data	Notes
Atkin-Lehner	2+ 53+	Signs for the Atkin-Lehner involutions
Class	106b	Isogeny class
Conductor	106	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	8	Modular degree for the optimal curve
Δ	-848 = -1 · 24 · 53	Discriminant
Eigenvalues	2+ -1 -4  0 -4  1  5 -7	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-7,5]	[a1,a2,a3,a4,a6]
Generators	[2:-3:1]	Generators of the group modulo torsion
j	-47045881/848	j-invariant
L	0.6909022750657	L(r)(E,1)/r!
Ω	5.0128820343348	Real period
R	0.068912680403558	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	848a1 3392e1 954m1 2650l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 106b1

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
+	-1	-4	0	-4	1	5	-7	1	5	-4	1	-10	-10	-6	+	-6	4	4	15	-8	1	-3	2	17

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Quadratic twists for elliptic curve 106b1

-4	8	-3	5	-7	-11	13	17	-19	-23	29	-31	53
848a1	3392e1	954m1	2650l1	5194f1	12826h1	17914h1	30634a1	38266k1	56074c1	89146d1	101866h1	5618f1

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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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