Cremona's table of elliptic curves

101728 = 2⁵ · 11 · 17²

Field	Data	Notes
Atkin-Lehner	2- 11- 17+	Signs for the Atkin-Lehner involutions
Class	101728n	Isogeny class
Conductor	101728	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	473088	Modular degree for the optimal curve
Δ	-131592619372544 = -1 · 212 · 113 · 176	Discriminant
Eigenvalues	2- -3 -1  0 11- -6 17+  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,2312,-550256]	[a1,a2,a3,a4,a6]
Generators	[544:12716:1]	Generators of the group modulo torsion
j	13824/1331	j-invariant
L	3.0590719049394	L(r)(E,1)/r!
Ω	0.27762420572896	Real period
R	0.91822922000332	Regulator
r	1	Rank of the group of rational points
S	1.0000000033908	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	101728k1 352e1	Quadratic twists by: -4 17

Hecke Eigenvalues for elliptic curve 101728n1

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
-	-3	-1	0	-	-6	+	6	-3	4	9	-7	2	6	12	2	9	-8	-15	3	6	6	-6	-5	3

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Quadratic twists for elliptic curve 101728n1

-4	17
101728k1	352e1

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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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