Properties

Label 108a
Number of curves 2
Conductor 108
CM -3
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("108.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 108a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
108.a2 108a1 [0, 0, 0, 0, 4] [3] 6 \(\Gamma_0(N)\)-optimal
108.a1 108a2 [0, 0, 0, 0, -108] [] 18  

Rank

sage: E.rank()
 

The elliptic curves in class 108a have rank \(0\).

Modular form 108.2.a.a

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.