Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("23120.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23120bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23120.i3 23120bj1 [0, 1, 0, -385, -2130] [2] 9216 \(\Gamma_0(N)\)-optimal
23120.i4 23120bj2 [0, 1, 0, 1060, -13112] [2] 18432  
23120.i1 23120bj3 [0, 1, 0, -11945, 498418] [2] 27648  
23120.i2 23120bj4 [0, 1, 0, -10500, 625000] [2] 55296  

Rank

sage: E.rank()
 

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

Modular form 23120.2.a.i

sage: E.q_eigenform(10)
 
\( q - 2q^{3} + q^{5} + 2q^{7} + q^{9} + 2q^{13} - 2q^{15} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.