Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("330.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 330.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
330.e1 330b5 [1, 0, 0, -3885, -93525] [2] 256  
330.e2 330b4 [1, 0, 0, -1175, 15405] [4] 128  
330.e3 330b3 [1, 0, 0, -255, -1323] [2, 2] 128  
330.e4 330b2 [1, 0, 0, -75, 225] [2, 4] 64  
330.e5 330b1 [1, 0, 0, 5, 17] [4] 32 \(\Gamma_0(N)\)-optimal
330.e6 330b6 [1, 0, 0, 495, -7473] [2] 256  

Rank

sage: E.rank()
 

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

Modular form 330.2.a.e

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.