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Properties

Label 56350.bb
Number of curves $2$
Conductor $56350$
CM no
Rank $2$
Graph

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

Elliptic curves in class 56350.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56350.bb1 56350br2 \([1, 0, 0, -7743, 604057]\) \(-17455277065/43606528\) \(-128256610316800\) \([]\) \(248832\) \(1.3950\)  
56350.bb2 56350br1 \([1, 0, 0, 832, -18488]\) \(21653735/63112\) \(-185626592200\) \([]\) \(82944\) \(0.84567\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 56350.bb have rank \(2\).

Complex multiplication

The elliptic curves in class 56350.bb do not have complex multiplication.

Modular form 56350.2.a.bb

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} + q^{4} - 2 q^{6} + q^{8} + q^{9} - 6 q^{11} - 2 q^{12} - q^{13} + q^{16} - 3 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.