Properties

Label 25200eg
Number of curves 8
Conductor 25200
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("25200.eh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 25200eg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25200.eh7 25200eg1 [0, 0, 0, -1791075, 922257250] [2] 442368 \(\Gamma_0(N)\)-optimal
25200.eh6 25200eg2 [0, 0, 0, -2079075, 605745250] [2, 2] 884736  
25200.eh5 25200eg3 [0, 0, 0, -5301075, -3570272750] [2] 1327104  
25200.eh8 25200eg4 [0, 0, 0, 6920925, 4448745250] [2] 1769472  
25200.eh4 25200eg5 [0, 0, 0, -15687075, -23494022750] [2] 1769472  
25200.eh2 25200eg6 [0, 0, 0, -79029075, -270391904750] [2, 2] 2654208  
25200.eh3 25200eg7 [0, 0, 0, -73269075, -311477984750] [2] 5308416  
25200.eh1 25200eg8 [0, 0, 0, -1264437075, -17305890272750] [2] 5308416  

Rank

sage: E.rank()
 

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

Modular form 25200.2.a.eh

sage: E.q_eigenform(10)
 
\( q + q^{7} - 2q^{13} - 6q^{17} - 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.