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Properties

Label 43350.bb
Number of curves $2$
Conductor $43350$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 43350.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43350.bb1 43350bv2 \([1, 0, 1, -9378201, -11054928452]\) \(33475791145/192\) \(523181808075000000\) \([]\) \(1982880\) \(2.5907\)  
43350.bb2 43350bv1 \([1, 0, 1, -166326, -678452]\) \(186745/108\) \(294289767042187500\) \([3]\) \(660960\) \(2.0414\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 43350.bb have rank \(0\).

Complex multiplication

The elliptic curves in class 43350.bb do not have complex multiplication.

Modular form 43350.2.a.bb

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.