Properties

Label 25872bp
Number of curves $2$
Conductor $25872$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bp1")
 
E.isogeny_class()
 

Elliptic curves in class 25872bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25872.e2 25872bp1 \([0, -1, 0, -50864, -4901952]\) \(-10358806345399/1445216256\) \(-2030424784109568\) \([2]\) \(129024\) \(1.6687\) \(\Gamma_0(N)\)-optimal
25872.e1 25872bp2 \([0, -1, 0, -839344, -295693376]\) \(46546832455691959/748268928\) \(1051263968477184\) \([2]\) \(258048\) \(2.0153\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 25872.2.a.bp

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