Properties

Label 25920.bx
Number of curves $2$
Conductor $25920$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bx1")
 
E.isogeny_class()
 

Elliptic curves in class 25920.bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25920.bx1 25920bf2 \([0, 0, 0, -14412, -668816]\) \(-15590912409/78125\) \(-1658880000000\) \([]\) \(43008\) \(1.1921\)  
25920.bx2 25920bf1 \([0, 0, 0, -12, 496]\) \(-9/5\) \(-106168320\) \([]\) \(6144\) \(0.21913\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 25920.bx have rank \(0\).

Complex multiplication

The elliptic curves in class 25920.bx do not have complex multiplication.

Modular form 25920.2.a.bx

sage: E.q_eigenform(10)
 
\(q + q^{5} - 3 q^{7} + 2 q^{11} + 2 q^{13} + 4 q^{17} + 8 q^{19} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.