Properties

Label 25200dx
Number of curves $6$
Conductor $25200$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("dx1")
 
E.isogeny_class()
 

Elliptic curves in class 25200dx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25200.cr6 25200dx1 \([0, 0, 0, 3525, -17750]\) \(103823/63\) \(-2939328000000\) \([2]\) \(32768\) \(1.0817\) \(\Gamma_0(N)\)-optimal
25200.cr5 25200dx2 \([0, 0, 0, -14475, -143750]\) \(7189057/3969\) \(185177664000000\) \([2, 2]\) \(65536\) \(1.4282\)  
25200.cr3 25200dx3 \([0, 0, 0, -140475, 20142250]\) \(6570725617/45927\) \(2142770112000000\) \([2]\) \(131072\) \(1.7748\)  
25200.cr2 25200dx4 \([0, 0, 0, -176475, -28493750]\) \(13027640977/21609\) \(1008189504000000\) \([2, 2]\) \(131072\) \(1.7748\)  
25200.cr4 25200dx5 \([0, 0, 0, -122475, -46259750]\) \(-4354703137/17294403\) \(-806887666368000000\) \([2]\) \(262144\) \(2.1214\)  
25200.cr1 25200dx6 \([0, 0, 0, -2822475, -1825127750]\) \(53297461115137/147\) \(6858432000000\) \([2]\) \(262144\) \(2.1214\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 25200dx do not have complex multiplication.

Modular form 25200.2.a.dx

sage: E.q_eigenform(10)
 
\(q - q^{7} + 4 q^{11} + 2 q^{13} - 6 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.