Properties

Label 30345.f
Number of curves 4
Conductor 30345
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("30345.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30345.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30345.f1 30345m4 [1, 1, 1, -487260, 130706322] [2] 294912  
30345.f2 30345m3 [1, 1, 1, -154910, -21879898] [2] 294912  
30345.f3 30345m2 [1, 1, 1, -32085, 1800762] [2, 2] 147456  
30345.f4 30345m1 [1, 1, 1, 4040, 167912] [4] 73728 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 30345.2.a.f

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.