Properties

Label 25872bz
Number of curves $2$
Conductor $25872$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bz1")
 
E.isogeny_class()
 

Elliptic curves in class 25872bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25872.k2 25872bz1 \([0, -1, 0, -3789, 105624]\) \(-3196715008/649539\) \(-1222681820976\) \([2]\) \(43200\) \(1.0417\) \(\Gamma_0(N)\)-optimal
25872.k1 25872bz2 \([0, -1, 0, -63324, 6154380]\) \(932410994128/29403\) \(885563788032\) \([2]\) \(86400\) \(1.3883\)  

Rank

sage: E.rank()
 

The elliptic curves in class 25872bz have rank \(0\).

Complex multiplication

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

Modular form 25872.2.a.bz

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} + q^{9} + q^{11} - 6 q^{13} + 2 q^{15} + 4 q^{17} - 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.