Properties

Label 148800.jc
Number of curves $6$
Conductor $148800$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("148800.jc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 148800.jc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
148800.jc1 148800hu6 [0, 1, 0, -492032033, -4201023743937] [2] 18874368  
148800.jc2 148800hu4 [0, 1, 0, -30752033, -65648543937] [2, 2] 9437184  
148800.jc3 148800hu5 [0, 1, 0, -30272033, -67796543937] [2] 18874368  
148800.jc4 148800hu3 [0, 1, 0, -5920033, 4320608063] [2] 9437184  
148800.jc5 148800hu2 [0, 1, 0, -1952033, -992543937] [2, 2] 4718592  
148800.jc6 148800hu1 [0, 1, 0, 95967, -64799937] [2] 2359296 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 148800.jc have rank \(0\).

Modular form 148800.2.a.jc

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.