Properties

Label 235200.bbn
Number of curves $6$
Conductor $235200$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("235200.bbn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 235200.bbn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
235200.bbn1 235200bbn5 [0, 1, 0, -51353633, 141625900863] [2] 18874368  
235200.bbn2 235200bbn3 [0, 1, 0, -3333633, 2031760863] [2, 2] 9437184  
235200.bbn3 235200bbn2 [0, 1, 0, -883633, -288389137] [2, 2] 4718592  
235200.bbn4 235200bbn1 [0, 1, 0, -859133, -306788637] [2] 2359296 \(\Gamma_0(N)\)-optimal
235200.bbn5 235200bbn4 [0, 1, 0, 1174367, -1430579137] [2] 9437184  
235200.bbn6 235200bbn6 [0, 1, 0, 5486367, 10966420863] [2] 18874368  

Rank

sage: E.rank()
 

The elliptic curves in class 235200.bbn have rank \(1\).

Modular form 235200.2.a.bbn

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.