Properties

Label 180a
Number of curves 4
Conductor 180
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("180.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 180a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
180.a3 180a1 [0, 0, 0, -12, -11] [2] 12 \(\Gamma_0(N)\)-optimal
180.a4 180a2 [0, 0, 0, 33, -74] [2] 24  
180.a1 180a3 [0, 0, 0, -372, 2761] [6] 36  
180.a2 180a4 [0, 0, 0, -327, 3454] [6] 72  

Rank

sage: E.rank()
 

The elliptic curves in class 180a have rank \(0\).

Modular form 180.2.a.a

sage: E.q_eigenform(10)
 
\( q + q^{5} + 2q^{7} + 2q^{13} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.