Properties

Label 246.a
Number of curves 2
Conductor 246
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("246.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 246.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
246.a1 246d1 [1, 1, 0, -66, 180] [2] 48 \(\Gamma_0(N)\)-optimal
246.a2 246d2 [1, 1, 0, -26, 444] [2] 96  

Rank

sage: E.rank()
 

The elliptic curves in class 246.a have rank \(1\).

Modular form 246.2.a.a

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.