Properties

Label 303450.ce
Number of curves 8
Conductor 303450
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("303450.ce1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 303450.ce

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
303450.ce1 303450ce8 [1, 0, 1, -13877780151, -629258247658052] [2] 251658240  
303450.ce2 303450ce6 [1, 0, 1, -867361401, -9832210970552] [2, 2] 125829120  
303450.ce3 303450ce7 [1, 0, 1, -861942651, -9961123033052] [2] 251658240  
303450.ce4 303450ce3 [1, 0, 1, -108880901, 437166760448] [2] 62914560  
303450.ce5 303450ce4 [1, 0, 1, -54548901, -151614095552] [2, 2] 62914560  
303450.ce6 303450ce2 [1, 0, 1, -7730901, 4851660448] [2, 2] 31457280  
303450.ce7 303450ce1 [1, 0, 1, 1517099, 542092448] [2] 15728640 \(\Gamma_0(N)\)-optimal
303450.ce8 303450ce5 [1, 0, 1, 9175599, -484638332552] [2] 125829120  

Rank

sage: E.rank()
 

The elliptic curves in class 303450.ce have rank \(0\).

Modular form 303450.2.a.ce

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

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.