Properties

Label 56550bv
Number of curves $4$
Conductor $56550$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 56550bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
56550.cg3 56550bv1 \([1, 0, 0, -44313, 3586617]\) \(615882348586441/21715200\) \(339300000000\) \([2]\) \(294912\) \(1.3023\) \(\Gamma_0(N)\)-optimal
56550.cg2 56550bv2 \([1, 0, 0, -46313, 3244617]\) \(703093388853961/115124490000\) \(1798820156250000\) \([2, 2]\) \(589824\) \(1.6489\)  
56550.cg4 56550bv3 \([1, 0, 0, 84187, 18252117]\) \(4223169036960119/11647532812500\) \(-181992700195312500\) \([2]\) \(1179648\) \(1.9955\)  
56550.cg1 56550bv4 \([1, 0, 0, -208813, -33642883]\) \(64443098670429961/6032611833300\) \(94259559895312500\) \([2]\) \(1179648\) \(1.9955\)  

Rank

sage: E.rank()
 

The elliptic curves in class 56550bv have rank \(0\).

Complex multiplication

The elliptic curves in class 56550bv do not have complex multiplication.

Modular form 56550.2.a.bv

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + 4 q^{7} + q^{8} + q^{9} - 4 q^{11} + q^{12} - q^{13} + 4 q^{14} + q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + O(q^{20})\)  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 Cremona 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 Cremona labels.