Cremona's table of elliptic curves

33856 = 2⁶ · 23²

Field	Data	Notes
Atkin-Lehner	2- 23-	Signs for the Atkin-Lehner involutions
Class	33856bd	Isogeny class
Conductor	33856	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-7377521301352448 = -1 · 212 · 239	Discriminant
Eigenvalues	2-  0 -4  0  0 -6 -8  0	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,48668,0]	[a1,a2,a3,a4,a6]
Generators	[2:312:1]	Generators of the group modulo torsion
j	1728	j-invariant
L	2.1774334738461	L(r)(E,1)/r!
Ω	0.24965849216898	Real period
R	4.3608239698343	Regulator
r	1	Rank of the group of rational points
S	0.9999999999999	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	33856bd2 16928a1 33856bb2	Quadratic twists by: -4 8 -23

Hecke Eigenvalues for elliptic curve 33856bd2

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	0	0	-6	-8	0	-	-10	0	12	10	0	0	-4	0	-12	0	0	6	0	0	16	-8

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Quadratic twists for elliptic curve 33856bd2

-4	8	-23
33856bd2	16928a1	33856bb2

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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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