Properties

Label 11840.bh
Number of curves $4$
Conductor $11840$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bh1")
 
E.isogeny_class()
 

Elliptic curves in class 11840.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11840.bh1 11840c3 \([0, -1, 0, -337601, -75388735]\) \(16232905099479601/4052240\) \(1062270402560\) \([2]\) \(55296\) \(1.6832\)  
11840.bh2 11840c4 \([0, -1, 0, -336321, -75990079]\) \(-16048965315233521/256572640900\) \(-67258978376089600\) \([2]\) \(110592\) \(2.0298\)  
11840.bh3 11840c1 \([0, -1, 0, -4801, -68415]\) \(46694890801/18944000\) \(4966055936000\) \([2]\) \(18432\) \(1.1339\) \(\Gamma_0(N)\)-optimal
11840.bh4 11840c2 \([0, -1, 0, 15679, -514879]\) \(1625964918479/1369000000\) \(-358875136000000\) \([2]\) \(36864\) \(1.4805\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11840.bh have rank \(1\).

Complex multiplication

The elliptic curves in class 11840.bh do not have complex multiplication.

Modular form 11840.2.a.bh

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.