Properties

Label 330.d
Number of curves 6
Conductor 330
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("330.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 330.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
330.d1 330c5 [1, 1, 1, -171085, -27308713] [2] 1536  
330.d2 330c4 [1, 1, 1, -11825, 488927] [4] 768  
330.d3 330c3 [1, 1, 1, -10705, -429025] [2, 2] 768  
330.d4 330c6 [1, 1, 1, -5205, -862425] [2] 1536  
330.d5 330c2 [1, 1, 1, -1025, 767] [2, 4] 384  
330.d6 330c1 [1, 1, 1, 255, 255] [4] 192 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 330.d have rank \(0\).

Modular form 330.2.a.d

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} + q^{11} - q^{12} + 6q^{13} - q^{15} + q^{16} + 2q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.