Properties

Label 25872q
Number of curves $4$
Conductor $25872$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 25872q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25872.br4 25872q1 \([0, 1, 0, 1356, -760068]\) \(9148592/8301447\) \(-250024176154368\) \([2]\) \(98304\) \(1.4417\) \(\Gamma_0(N)\)-optimal
25872.br3 25872q2 \([0, 1, 0, -117224, -15131964]\) \(1478729816932/38900169\) \(4686403566265344\) \([2, 2]\) \(196608\) \(1.7883\)  
25872.br2 25872q3 \([0, 1, 0, -268144, 31653236]\) \(8849350367426/3314597517\) \(798636202552387584\) \([4]\) \(393216\) \(2.1349\)  
25872.br1 25872q4 \([0, 1, 0, -1863584, -979821228]\) \(2970658109581346/2139291\) \(515451795167232\) \([2]\) \(393216\) \(2.1349\)  

Rank

sage: E.rank()
 

The elliptic curves in class 25872q have rank \(1\).

Complex multiplication

The elliptic curves in class 25872q do not have complex multiplication.

Modular form 25872.2.a.q

sage: E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{5} + q^{9} - q^{11} - 6 q^{13} - 2 q^{15} - 6 q^{17} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.