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Properties

Label 303450.bb
Number of curves $6$
Conductor $303450$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("303450.bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 303450.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
303450.bb1 303450bb6 [1, 1, 0, -121380150, -514768889250] [2] 31457280  
303450.bb2 303450bb4 [1, 1, 0, -7586400, -8045320500] [2, 2] 15728640  
303450.bb3 303450bb5 [1, 1, 0, -7080650, -9163533750] [2] 31457280  
303450.bb4 303450bb3 [1, 1, 0, -2673400, 1589072500] [2] 15728640  
303450.bb5 303450bb2 [1, 1, 0, -505900, -108080000] [2, 2] 7864320  
303450.bb6 303450bb1 [1, 1, 0, 72100, -10398000] [2] 3932160 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 303450.bb have rank \(2\).

Modular form 303450.2.a.bb

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.