Properties

Label 720i
Number of curves 4
Conductor 720
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath

sage: E = EllipticCurve("720.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 720i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
720.h3 720i1 [0, 0, 0, -12, 11] [2] 48 \(\Gamma_0(N)\)-optimal
720.h4 720i2 [0, 0, 0, 33, 74] [2] 96  
720.h1 720i3 [0, 0, 0, -372, -2761] [2] 144  
720.h2 720i4 [0, 0, 0, -327, -3454] [2] 288  

Rank

sage: E.rank()
 

The elliptic curves in class 720i have rank \(0\).

Modular form 720.2.a.h

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.