Cremona's table of elliptic curves

1856 = 2⁶ · 29

Field	Data	Notes
Atkin-Lehner	2- 29-	Signs for the Atkin-Lehner involutions
Class	1856m	Isogeny class
Conductor	1856	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	-1900544 = -1 · 216 · 29	Discriminant
Eigenvalues	2- -1  3 -2 -3  5 -4  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,31,1]	[a1,a2,a3,a4,a6]
Generators	[5:16:1]	Generators of the group modulo torsion
j	48668/29	j-invariant
L	2.7663643426983	L(r)(E,1)/r!
Ω	1.6079950027991	Real period
R	0.43009529536516	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	1856b1 464a1 16704cu1 46400bv1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1856m1

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	3	-2	-3	5	-4	0	0	-	-9	-8	-2	-11	7	-9	4	12	12	-2	-4	-3	-16	2	-14

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Quadratic twists for elliptic curve 1856m1

-4	8	-3	5	-7	29
1856b1	464a1	16704cu1	46400bv1	90944du1	53824v1

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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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