Properties

Label 119952.bh
Number of curves 6
Conductor 119952
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("119952.bh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 119952.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
119952.bh1 119952gt6 [0, 0, 0, -195761811, 1054241418706] [2] 9437184  
119952.bh2 119952gt4 [0, 0, 0, -12235251, 16472132530] [2, 2] 4718592  
119952.bh3 119952gt5 [0, 0, 0, -11600211, 18258246034] [2] 9437184  
119952.bh4 119952gt2 [0, 0, 0, -804531, 229079410] [2, 2] 2359296  
119952.bh5 119952gt1 [0, 0, 0, -240051, -41983886] [2] 1179648 \(\Gamma_0(N)\)-optimal
119952.bh6 119952gt3 [0, 0, 0, 1594509, 1334077234] [2] 4718592  

Rank

sage: E.rank()
 

The elliptic curves in class 119952.bh have rank \(1\).

Modular form 119952.2.a.bh

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.