Properties

Label 14700.bn
Number of curves $2$
Conductor $14700$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bn1")
 
E.isogeny_class()
 

Elliptic curves in class 14700.bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14700.bn1 14700bg2 \([0, 1, 0, -1108, 12788]\) \(109744/9\) \(12348000000\) \([2]\) \(12288\) \(0.67894\)  
14700.bn2 14700bg1 \([0, 1, 0, -233, -1212]\) \(16384/3\) \(257250000\) \([2]\) \(6144\) \(0.33237\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 14700.bn have rank \(0\).

Complex multiplication

The elliptic curves in class 14700.bn do not have complex multiplication.

Modular form 14700.2.a.bn

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} + 2 q^{11} - 4 q^{13} + 6 q^{17} - 8 q^{19} + O(q^{20})\) 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.