Properties

Label 116025.bh
Number of curves $2$
Conductor $116025$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 116025.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116025.bh1 116025c1 \([1, 1, 0, -11375, 462000]\) \(10418796526321/6390657\) \(99854015625\) \([2]\) \(179200\) \(1.0534\) \(\Gamma_0(N)\)-optimal
116025.bh2 116025c2 \([1, 1, 0, -9250, 642625]\) \(-5602762882081/8312741073\) \(-129886579265625\) \([2]\) \(358400\) \(1.3999\)  

Rank

sage: E.rank()
 

The elliptic curves in class 116025.bh have rank \(1\).

Complex multiplication

The elliptic curves in class 116025.bh do not have complex multiplication.

Modular form 116025.2.a.bh

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} - q^{6} - q^{7} - 3q^{8} + q^{9} - 4q^{11} + q^{12} - q^{13} - q^{14} - q^{16} - q^{17} + q^{18} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.