Cremona's table of elliptic curves

101568 = 2⁶ · 3 · 23²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 23-	Signs for the Atkin-Lehner involutions
Class	101568m	Isogeny class
Conductor	101568	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	270336	Modular degree for the optimal curve
Δ	-125515485278208 = -1 · 212 · 32 · 237	Discriminant
Eigenvalues	2+ 3+ -2 -2  2 -6  0 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,11991,183465]	[a1,a2,a3,a4,a6]
Generators	[-3:384:1] [8:529:1]	Generators of the group modulo torsion
j	314432/207	j-invariant
L	7.844122795657	L(r)(E,1)/r!
Ω	0.36774688679325	Real period
R	2.666277770574	Regulator
r	2	Rank of the group of rational points
S	1.0000000000026	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	101568bl1 50784n1 4416d1	Quadratic twists by: -4 8 -23

Hecke Eigenvalues for elliptic curve 101568m1

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
+	+	-2	-2	2	-6	0	-4	-	-2	4	8	-6	0	0	-6	-12	12	8	0	-10	-14	6	0	-10

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Quadratic twists for elliptic curve 101568m1

-4	8	-23
101568bl1	50784n1	4416d1

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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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