Properties

Label 30345.d
Number of curves 6
Conductor 30345
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("30345.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30345.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30345.d1 30345g6 [1, 1, 1, -6696136, -6672050806] [2] 1179648  
30345.d2 30345g4 [1, 1, 1, -1654531, 818440778] [2] 589824  
30345.d3 30345g3 [1, 1, 1, -432061, -97277686] [2, 2] 589824  
30345.d4 30345g2 [1, 1, 1, -106936, 11834264] [2, 2] 294912  
30345.d5 30345g1 [1, 1, 1, 10109, 972488] [2] 147456 \(\Gamma_0(N)\)-optimal
30345.d6 30345g5 [1, 1, 1, 630014, -499166866] [2] 1179648  

Rank

sage: E.rank()
 

The elliptic curves in class 30345.d have rank \(0\).

Modular form 30345.2.a.d

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + q^{7} + 3q^{8} + q^{9} + q^{10} - 4q^{11} + q^{12} + 6q^{13} - q^{14} + q^{15} - q^{16} - q^{18} - 4q^{19} + O(q^{20}) \)

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 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.