Properties

Label 30446.a
Number of curves 3
Conductor 30446
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("30446.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30446.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30446.a1 30446f3 [1, 0, 1, -3795071, -2955377838] [] 1003104  
30446.a2 30446f1 [1, 0, 1, -35601, 2916644] [3] 111456 \(\Gamma_0(N)\)-optimal
30446.a3 30446f2 [1, 0, 1, 239024, -10823394] [3] 334368  

Rank

sage: E.rank()
 

The elliptic curves in class 30446.a have rank \(1\).

Modular form 30446.2.a.a

sage: E.q_eigenform(10)
 
\( q - q^{2} - 2q^{3} + q^{4} + 2q^{6} - q^{7} - q^{8} + q^{9} + 3q^{11} - 2q^{12} + q^{13} + q^{14} + q^{16} - 3q^{17} - q^{18} + 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.