Properties

Label 11830l
Number of curves $4$
Conductor $11830$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("11830.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11830l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11830.h4 11830l1 [1, -1, 0, 391, -4835] [2] 7680 \(\Gamma_0(N)\)-optimal
11830.h3 11830l2 [1, -1, 0, -2989, -50127] [2, 2] 15360  
11830.h1 11830l3 [1, -1, 0, -45239, -3692077] [2] 30720  
11830.h2 11830l4 [1, -1, 0, -14819, 652575] [2] 30720  

Rank

sage: E.rank()
 

The elliptic curves in class 11830l have rank \(1\).

Modular form 11830.2.a.h

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - 3q^{9} - q^{10} - 4q^{11} - q^{14} + q^{16} + 2q^{17} + 3q^{18} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.