Properties

Label 25200.fq
Number of curves $6$
Conductor $25200$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("25200.fq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 25200.fq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25200.fq1 25200er6 [0, 0, 0, -60480075, -181036687750] [2] 1179648  
25200.fq2 25200er4 [0, 0, 0, -3780075, -2828587750] [2, 2] 589824  
25200.fq3 25200er5 [0, 0, 0, -3528075, -3221959750] [2] 1179648  
25200.fq4 25200er3 [0, 0, 0, -1332075, 559300250] [4] 589824  
25200.fq5 25200er2 [0, 0, 0, -252075, -37939750] [2, 2] 294912  
25200.fq6 25200er1 [0, 0, 0, 35925, -3667750] [2] 147456 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 25200.fq have rank \(0\).

Modular form 25200.2.a.fq

sage: E.q_eigenform(10)
 
\( q + q^{7} + 4q^{11} + 2q^{13} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.