Properties

Label 244800ip
Number of curves 6
Conductor 244800
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("244800.ip1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 244800ip

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
244800.ip5 244800ip1 [0, 0, 0, -489900, -122402000] [2] 3145728 \(\Gamma_0(N)\)-optimal
244800.ip4 244800ip2 [0, 0, 0, -1641900, 667870000] [2, 2] 6291456  
244800.ip2 244800ip3 [0, 0, 0, -24969900, 48023710000] [2, 2] 12582912  
244800.ip6 244800ip4 [0, 0, 0, 3254100, 3889438000] [2] 12582912  
244800.ip1 244800ip5 [0, 0, 0, -399513900, 3073590142000] [2] 25165824  
244800.ip3 244800ip6 [0, 0, 0, -23673900, 53231038000] [2] 25165824  

Rank

sage: E.rank()
 

The elliptic curves in class 244800ip have rank \(1\).

Modular form 244800.2.a.ip

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

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.