Properties

Label 25200dz
Number of curves 8
Conductor 25200
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("25200.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 25200dz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25200.p7 25200dz1 [0, 0, 0, 755925, 190620250] [2] 589824 \(\Gamma_0(N)\)-optimal
25200.p6 25200dz2 [0, 0, 0, -3852075, 1706652250] [2, 2] 1179648  
25200.p5 25200dz3 [0, 0, 0, -27180075, -53324099750] [2, 2] 2359296  
25200.p4 25200dz4 [0, 0, 0, -54252075, 153763452250] [2] 2359296  
25200.p8 25200dz5 [0, 0, 0, 4571925, -170457227750] [2] 4718592  
25200.p2 25200dz6 [0, 0, 0, -432180075, -3458159099750] [2, 2] 4718592  
25200.p3 25200dz7 [0, 0, 0, -429480075, -3503500199750] [2] 9437184  
25200.p1 25200dz8 [0, 0, 0, -6914880075, -221322257999750] [2] 9437184  

Rank

sage: E.rank()
 

The elliptic curves in class 25200dz have rank \(1\).

Modular form 25200.2.a.p

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 Cremona numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 8 & 8 \\ 8 & 4 & 2 & 8 & 4 & 1 & 2 & 2 \\ 16 & 8 & 4 & 16 & 8 & 2 & 1 & 4 \\ 16 & 8 & 4 & 16 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.