Properties

Label 54450l
Number of curves $4$
Conductor $54450$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 54450l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
54450.cp4 54450l1 \([1, -1, 0, 17583, -248759]\) \(804357/500\) \(-373688648437500\) \([2]\) \(207360\) \(1.4853\) \(\Gamma_0(N)\)-optimal
54450.cp3 54450l2 \([1, -1, 0, -73167, -1973009]\) \(57960603/31250\) \(23355540527343750\) \([2]\) \(414720\) \(1.8319\)  
54450.cp2 54450l3 \([1, -1, 0, -209292, 42025616]\) \(-1860867/320\) \(-174348175815000000\) \([2]\) \(622080\) \(2.0346\)  
54450.cp1 54450l4 \([1, -1, 0, -3476292, 2495542616]\) \(8527173507/200\) \(108967609884375000\) \([2]\) \(1244160\) \(2.3812\)  

Rank

sage: E.rank()
 

The elliptic curves in class 54450l have rank \(0\).

Complex multiplication

The elliptic curves in class 54450l do not have complex multiplication.

Modular form 54450.2.a.l

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.