Properties

Label 25200ea
Number of curves $4$
Conductor $25200$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("25200.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 25200ea

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25200.o3 25200ea1 [0, 0, 0, -12675, -346750] [2] 73728 \(\Gamma_0(N)\)-optimal
25200.o2 25200ea2 [0, 0, 0, -84675, 9229250] [2, 2] 147456  
25200.o4 25200ea3 [0, 0, 0, 23325, 31153250] [2] 294912  
25200.o1 25200ea4 [0, 0, 0, -1344675, 600169250] [2] 294912  

Rank

sage: E.rank()
 

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

Modular form 25200.2.a.o

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.