Properties

Label 145.a
Number of curves 2
Conductor 145
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("145.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 145.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
145.a1 145a1 [1, -1, 1, -3, 2] [2] 4 \(\Gamma_0(N)\)-optimal
145.a2 145a2 [1, -1, 1, 2, 6] [2] 8  

Rank

sage: E.rank()
 

The elliptic curves in class 145.a have rank \(1\).

Modular form 145.2.a.a

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.