Properties

Label 301665.bm
Number of curves $4$
Conductor $301665$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bm1")
 
E.isogeny_class()
 

Elliptic curves in class 301665.bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
301665.bm1 301665bm3 \([1, 1, 0, -171538, 21030937]\) \(115650783909361/27072079335\) \(130671756182892015\) \([2]\) \(3538944\) \(1.9961\)  
301665.bm2 301665bm2 \([1, 1, 0, -57463, -5046608]\) \(4347507044161/258084225\) \(1245723259988025\) \([2, 2]\) \(1769472\) \(1.6495\)  
301665.bm3 301665bm1 \([1, 1, 0, -56618, -5209017]\) \(4158523459441/16065\) \(77542686585\) \([2]\) \(884736\) \(1.3030\) \(\Gamma_0(N)\)-optimal
301665.bm4 301665bm4 \([1, 1, 0, 43092, -20713077]\) \(1833318007919/39525924375\) \(-190784087506569375\) \([2]\) \(3538944\) \(1.9961\)  

Rank

sage: E.rank()
 

The elliptic curves in class 301665.bm have rank \(0\).

Complex multiplication

The elliptic curves in class 301665.bm do not have complex multiplication.

Modular form 301665.2.a.bm

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} - q^{5} - q^{6} - q^{7} - 3 q^{8} + q^{9} - q^{10} - 4 q^{11} + q^{12} - q^{14} + q^{15} - q^{16} + q^{17} + q^{18} - 8 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.