Properties

Label 121680.bt
Number of curves $2$
Conductor $121680$
CM no
Rank $1$
Graph

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

Elliptic curves in class 121680.bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
121680.bt1 121680dq2 \([0, 0, 0, -1119963, -408672758]\) \(10779215329/1232010\) \(17756682244053442560\) \([2]\) \(3096576\) \(2.4259\)  
121680.bt2 121680dq1 \([0, 0, 0, 96837, -32194838]\) \(6967871/35100\) \(-505888383021465600\) \([2]\) \(1548288\) \(2.0793\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 121680.bt have rank \(1\).

Complex multiplication

The elliptic curves in class 121680.bt do not have complex multiplication.

Modular form 121680.2.a.bt

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