Properties

Label 11760bo
Number of curves $2$
Conductor $11760$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("11760.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11760bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11760.f1 11760bo1 [0, -1, 0, -11776, -184064] [2] 32256 \(\Gamma_0(N)\)-optimal
11760.f2 11760bo2 [0, -1, 0, 43104, -1457280] [2] 64512  

Rank

sage: E.rank()
 

The elliptic curves in class 11760bo have rank \(1\).

Modular form 11760.2.a.f

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} + q^{9} - 2q^{11} - 2q^{13} + q^{15} + 4q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.