Properties

Label 23120a
Number of curves 4
Conductor 23120
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("23120.r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23120a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23120.r3 23120a1 [0, 0, 0, -578, -4913] [2] 10240 \(\Gamma_0(N)\)-optimal
23120.r2 23120a2 [0, 0, 0, -2023, 29478] [2, 2] 20480  
23120.r4 23120a3 [0, 0, 0, 3757, 167042] [2] 40960  
23120.r1 23120a4 [0, 0, 0, -30923, 2092938] [2] 40960  

Rank

sage: E.rank()
 

The elliptic curves in class 23120a have rank \(1\).

Modular form 23120.2.a.r

sage: E.q_eigenform(10)
 
\( q - q^{5} - 4q^{7} - 3q^{9} + 4q^{11} - 2q^{13} - 4q^{19} + O(q^{20}) \)

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.