Properties

Label 4335d
Number of curves 8
Conductor 4335
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("4335.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4335d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4335.c7 4335d1 [1, 0, 0, -6, 915] [2] 1280 \(\Gamma_0(N)\)-optimal
4335.c6 4335d2 [1, 0, 0, -1451, 20856] [2, 2] 2560  
4335.c5 4335d3 [1, 0, 0, -2896, -27985] [2, 2] 5120  
4335.c4 4335d4 [1, 0, 0, -23126, 1351701] [2] 5120  
4335.c2 4335d5 [1, 0, 0, -39021, -2968560] [2, 2] 10240  
4335.c8 4335d6 [1, 0, 0, 10109, -207454] [2] 10240  
4335.c1 4335d7 [1, 0, 0, -624246, -189889425] [2] 20480  
4335.c3 4335d8 [1, 0, 0, -31796, -4099995] [2] 20480  

Rank

sage: E.rank()
 

The elliptic curves in class 4335d have rank \(0\).

Modular form 4335.2.a.c

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} - q^{4} - q^{5} - q^{6} + 3q^{8} + q^{9} + q^{10} + 4q^{11} - q^{12} - 2q^{13} - q^{15} - q^{16} - q^{18} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.