Properties

Label 304920.ch
Number of curves $6$
Conductor $304920$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("304920.ch1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 304920.ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
304920.ch1 304920ch6 [0, 0, 0, -11413083, -14840306602] [2] 10485760  
304920.ch2 304920ch4 [0, 0, 0, -740883, -212989282] [2, 2] 5242880  
304920.ch3 304920ch2 [0, 0, 0, -196383, 30184418] [2, 2] 2621440  
304920.ch4 304920ch1 [0, 0, 0, -190938, 32113037] [2] 1310720 \(\Gamma_0(N)\)-optimal
304920.ch5 304920ch3 [0, 0, 0, 260997, 149926502] [2] 5242880  
304920.ch6 304920ch5 [0, 0, 0, 1219317, -1148788762] [2] 10485760  

Rank

sage: E.rank()
 

The elliptic curves in class 304920.ch have rank \(1\).

Modular form 304920.2.a.ch

sage: E.q_eigenform(10)
 
\( q - q^{5} + q^{7} + 2q^{13} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.