Properties

Label 333795.bm
Number of curves $4$
Conductor $333795$
CM no
Rank $0$
Graph

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

Elliptic curves in class 333795.bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
333795.bm1 333795bm3 \([1, 1, 0, -166180063, 824479800718]\) \(21026497979043461623321/161783881875\) \(3905069611845661875\) \([2]\) \(39321600\) \(3.1599\)  
333795.bm2 333795bm2 \([1, 1, 0, -10393168, 12861235147]\) \(5143681768032498601/14238434358225\) \(343681191773626655025\) \([2, 2]\) \(19660800\) \(2.8133\)  
333795.bm3 333795bm4 \([1, 1, 0, -6296593, 23108407852]\) \(-1143792273008057401/8897444448004035\) \(-214762679287364307090915\) \([2]\) \(39321600\) \(3.1599\)  
333795.bm4 333795bm1 \([1, 1, 0, -912523, 22545688]\) \(3481467828171481/2005331497785\) \(48403827395658784665\) \([2]\) \(9830400\) \(2.4667\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 333795.bm have rank \(0\).

Complex multiplication

The elliptic curves in class 333795.bm do not have complex multiplication.

Modular form 333795.2.a.bm

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} - q^{5} - q^{6} - q^{7} - 3 q^{8} + q^{9} - q^{10} + q^{11} + q^{12} + 6 q^{13} - q^{14} + q^{15} - q^{16} + q^{18} + 4 q^{19} + O(q^{20})\) 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.