Properties

Label 720j
Number of curves 8
Conductor 720
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("720.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 720j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
720.j8 720j1 [0, 0, 0, 213, 3674] [2] 384 \(\Gamma_0(N)\)-optimal
720.j6 720j2 [0, 0, 0, -2667, 48026] [2, 2] 768  
720.j7 720j3 [0, 0, 0, -1947, -108214] [2] 1152  
720.j5 720j4 [0, 0, 0, -9867, -324934] [2] 1536  
720.j4 720j5 [0, 0, 0, -41547, 3259514] [4] 1536  
720.j3 720j6 [0, 0, 0, -48027, -4043446] [2, 2] 2304  
720.j1 720j7 [0, 0, 0, -768027, -259067446] [2] 4608  
720.j2 720j8 [0, 0, 0, -65307, -874294] [4] 4608  

Rank

sage: E.rank()
 

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

Modular form 720.2.a.j

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

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.