Properties

Label 30446.f
Number of curves 2
Conductor 30446
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("30446.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 30446.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
30446.f1 30446d2 [1, 0, 1, -103927, -1282982] [] 321408  
30446.f2 30446d1 [1, 0, 1, -67592, 6758038] [3] 107136 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 30446.2.a.f

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} + 3q^{5} - q^{6} - q^{7} - q^{8} - 2q^{9} - 3q^{10} + 3q^{11} + q^{12} + q^{13} + q^{14} + 3q^{15} + q^{16} - 6q^{17} + 2q^{18} + 2q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.