Properties

Label 58800ix
Number of curves $6$
Conductor $58800$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("58800.jt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 58800ix

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58800.jt5 58800ix1 [0, 1, 0, -78808, 18778388] [2] 589824 \(\Gamma_0(N)\)-optimal
58800.jt4 58800ix2 [0, 1, 0, -1646808, 812186388] [2, 2] 1179648  
58800.jt3 58800ix3 [0, 1, 0, -2038808, 395882388] [2, 2] 2359296  
58800.jt1 58800ix4 [0, 1, 0, -26342808, 52031690388] [2] 2359296  
58800.jt6 58800ix5 [0, 1, 0, 7565192, 3065794388] [2] 4718592  
58800.jt2 58800ix6 [0, 1, 0, -17914808, -28911213612] [2] 4718592  

Rank

sage: E.rank()
 

The elliptic curves in class 58800ix have rank \(0\).

Modular form 58800.2.a.jt

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.