Properties

Label 1856.n
Number of curves $2$
Conductor $1856$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 1856.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1856.n1 1856n1 \([0, -1, 0, -37, -75]\) \(5619712/29\) \(29696\) \([2]\) \(240\) \(-0.29599\) \(\Gamma_0(N)\)-optimal
1856.n2 1856n2 \([0, -1, 0, -17, -175]\) \(-35152/841\) \(-13778944\) \([2]\) \(480\) \(0.050583\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1856.n have rank \(1\).

Complex multiplication

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

Modular form 1856.2.a.n

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + 2 q^{5} - 4 q^{7} + q^{9} - 6 q^{11} - 2 q^{13} + 4 q^{15} + 2 q^{17} - 6 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.