Properties

Label 148720bb
Number of curves 4
Conductor 148720
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("148720.bq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 148720bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
148720.bq4 148720bb1 [0, -1, 0, -7661, -250264] [2] 311040 \(\Gamma_0(N)\)-optimal
148720.bq3 148720bb2 [0, -1, 0, -16956, 485900] [2] 622080  
148720.bq2 148720bb3 [0, -1, 0, -75261, 7871876] [2] 933120  
148720.bq1 148720bb4 [0, -1, 0, -1199956, 506336700] [2] 1866240  

Rank

sage: E.rank()
 

The elliptic curves in class 148720bb have rank \(0\).

Modular form 148720.2.a.bq

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

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 Cremona 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 Cremona labels.