Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("25200.eu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 25200.eu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25200.eu1 25200eh6 [0, 0, 0, -9829875, -11862332750] [2] 497664  
25200.eu2 25200eh5 [0, 0, 0, -613875, -185660750] [2] 248832  
25200.eu3 25200eh4 [0, 0, 0, -127875, -14426750] [2] 165888  
25200.eu4 25200eh2 [0, 0, 0, -37875, 2835250] [2] 55296  
25200.eu5 25200eh1 [0, 0, 0, -1875, 63250] [2] 27648 \(\Gamma_0(N)\)-optimal
25200.eu6 25200eh3 [0, 0, 0, 16125, -1322750] [2] 82944  

Rank

sage: E.rank()
 

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

Modular form 25200.2.a.eu

sage: E.q_eigenform(10)
 
\( q + q^{7} + 4q^{13} + 6q^{17} - 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.