Properties

Label 57330bt
Number of curves $2$
Conductor $57330$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 57330bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
57330.h2 57330bt1 \([1, -1, 0, 1755, -78975]\) \(6967871/35100\) \(-3010390847100\) \([2]\) \(138240\) \(1.0766\) \(\Gamma_0(N)\)-optimal
57330.h1 57330bt2 \([1, -1, 0, -20295, -991845]\) \(10779215329/1232010\) \(105664718733210\) \([2]\) \(276480\) \(1.4232\)  

Rank

sage: E.rank()
 

The elliptic curves in class 57330bt have rank \(0\).

Complex multiplication

The elliptic curves in class 57330bt do not have complex multiplication.

Modular form 57330.2.a.bt

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 4q^{11} + q^{13} + q^{16} + 8q^{17} + 6q^{19} + O(q^{20})\)  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 Cremona 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 Cremona labels.