Properties

Label 27930ch
Number of curves $4$
Conductor $27930$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("27930.ca1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 27930ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
27930.ca4 27930ch1 [1, 1, 1, -491, -7351] [2] 27648 \(\Gamma_0(N)\)-optimal
27930.ca3 27930ch2 [1, 1, 1, -9311, -349567] [2, 2] 55296  
27930.ca2 27930ch3 [1, 1, 1, -10781, -233731] [2] 110592  
27930.ca1 27930ch4 [1, 1, 1, -148961, -22190827] [2] 110592  

Rank

sage: E.rank()
 

The elliptic curves in class 27930ch have rank \(0\).

Modular form 27930.2.a.ca

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + q^{8} + q^{9} - q^{10} - 4q^{11} - q^{12} + 2q^{13} + q^{15} + q^{16} + 2q^{17} + q^{18} + q^{19} + O(q^{20}) \)

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.