Properties

Label 9360.bh
Number of curves $2$
Conductor $9360$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9360.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9360.bh1 9360bw2 \([0, 0, 0, -6627, -186014]\) \(10779215329/1232010\) \(3678762147840\) \([2]\) \(18432\) \(1.1434\)  
9360.bh2 9360bw1 \([0, 0, 0, 573, -14654]\) \(6967871/35100\) \(-104808038400\) \([2]\) \(9216\) \(0.79684\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9360.bh have rank \(0\).

Complex multiplication

The elliptic curves in class 9360.bh do not have complex multiplication.

Modular form 9360.2.a.bh

sage: E.q_eigenform(10)
 
\(q + q^{5} - 2q^{7} + 4q^{11} - q^{13} - 8q^{17} + 6q^{19} + O(q^{20})\)  Toggle raw display

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.