Properties

Label 24255bs
Number of curves $6$
Conductor $24255$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 24255bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
24255.bq6 24255bs1 [1, -1, 0, 15426, -214219265] [2] 368640 \(\Gamma_0(N)\)-optimal
24255.bq5 24255bs2 [1, -1, 0, -5278779, -4584056072] [2, 2] 737280  
24255.bq4 24255bs3 [1, -1, 0, -11221254, 7632484033] [2] 1474560  
24255.bq2 24255bs4 [1, -1, 0, -84043584, -296533682285] [2, 2] 1474560  
24255.bq3 24255bs5 [1, -1, 0, -83626839, -299620345802] [4] 2949120  
24255.bq1 24255bs6 [1, -1, 0, -1344697209, -18979168274060] [2] 2949120  

Rank

sage: E.rank()
 

The elliptic curves in class 24255bs have rank \(1\).

Complex multiplication

The elliptic curves in class 24255bs do not have complex multiplication.

Modular form 24255.2.a.bs

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} + q^{5} - 3q^{8} + q^{10} + q^{11} + 2q^{13} - q^{16} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.