Properties

Label 89930.bh
Number of curves $2$
Conductor $89930$
CM no
Rank $1$
Graph

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

Elliptic curves in class 89930.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
89930.bh1 89930bg2 \([1, 0, 0, -3513100, 2615874832]\) \(-32391289681150609/1228250000000\) \(-181825080664250000000\) \([]\) \(2993760\) \(2.6575\)  
89930.bh2 89930bg1 \([1, 0, 0, 211060, 11603600]\) \(7023836099951/4456448000\) \(-659714241462272000\) \([]\) \(997920\) \(2.1082\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 89930.bh have rank \(1\).

Complex multiplication

The elliptic curves in class 89930.bh do not have complex multiplication.

Modular form 89930.2.a.bh

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - 2 q^{7} + q^{8} - 2 q^{9} + q^{10} + q^{12} - q^{13} - 2 q^{14} + q^{15} + q^{16} + q^{17} - 2 q^{18} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.