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	101568ct	Isogeny class
Conductor	101568	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	811008	Modular degree for the optimal curve
Δ	-32131964231221248 = -1 · 220 · 32 · 237	Discriminant
Eigenvalues	2- 3+ -2 -2  6  2  0  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-51489,9743553]	[a1,a2,a3,a4,a6]
Generators	[-163:3712:1]	Generators of the group modulo torsion
j	-389017/828	j-invariant
L	4.6787701507065	L(r)(E,1)/r!
Ω	0.32867467960086	Real period
R	3.5588154831784	Regulator
r	1	Rank of the group of rational points
S	0.99999999913172	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	101568bm1 25392bc1 4416u1	Quadratic twists by: -4 8 -23

Hecke Eigenvalues for elliptic curve 101568ct1

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

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Quadratic twists for elliptic curve 101568ct1

-4	8	-23
101568bm1	25392bc1	4416u1

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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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