Properties

Label 1856.k
Number of curves $2$
Conductor $1856$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1856.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1856.k1 1856a2 \([0, 1, 0, -29121, -1935457]\) \(-10418796526321/82044596\) \(-21507498573824\) \([]\) \(3840\) \(1.3869\)  
1856.k2 1856a1 \([0, 1, 0, 319, 3743]\) \(13651919/29696\) \(-7784628224\) \([]\) \(768\) \(0.58217\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1856.k have rank \(0\).

Complex multiplication

The elliptic curves in class 1856.k do not have complex multiplication.

Modular form 1856.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - 2 q^{7} - 2 q^{9} + 3 q^{11} + q^{13} - q^{15} + 8 q^{17} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.