Properties

Label 720.b
Number of curves $4$
Conductor $720$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 720.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
720.b1 720f4 [0, 0, 0, -3483, 20682] [2] 1152  
720.b2 720f2 [0, 0, 0, -2043, -35542] [2] 384  
720.b3 720f1 [0, 0, 0, -123, -598] [2] 192 \(\Gamma_0(N)\)-optimal
720.b4 720f3 [0, 0, 0, 837, 2538] [2] 576  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 720.b do not have complex multiplication.

Modular form 720.2.a.b

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.