Properties

Label 25200eu
Number of curves $4$
Conductor $25200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("eu1")
 
E.isogeny_class()
 

Elliptic curves in class 25200eu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25200.dc4 25200eu1 \([0, 0, 0, 1500, -7625]\) \(2048000/1323\) \(-241116750000\) \([2]\) \(27648\) \(0.87295\) \(\Gamma_0(N)\)-optimal
25200.dc3 25200eu2 \([0, 0, 0, -6375, -62750]\) \(9826000/5103\) \(14880348000000\) \([2]\) \(55296\) \(1.2195\)  
25200.dc2 25200eu3 \([0, 0, 0, -25500, -1614125]\) \(-10061824000/352947\) \(-64324590750000\) \([2]\) \(82944\) \(1.4223\)  
25200.dc1 25200eu4 \([0, 0, 0, -411375, -101555750]\) \(2640279346000/3087\) \(9001692000000\) \([2]\) \(165888\) \(1.7688\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 25200.2.a.eu

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

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.