Properties

Label 236992.bh
Number of curves $2$
Conductor $236992$
CM no
Rank $0$
Graph

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

Elliptic curves in class 236992.bh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.bh1 236992bh2 \([0, 0, 0, -15817100, 23994686704]\) \(926859375/9604\) \(4534637733004090277888\) \([2]\) \(10174464\) \(2.9725\)  
236992.bh2 236992bh1 \([0, 0, 0, -243340, 926833392]\) \(-3375/784\) \(-370174508816660430848\) \([2]\) \(5087232\) \(2.6260\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 236992.bh have rank \(0\).

Complex multiplication

The elliptic curves in class 236992.bh do not have complex multiplication.

Modular form 236992.2.a.bh

sage: E.q_eigenform(10)
 
\(q - q^{7} - 3q^{9} - 4q^{11} + 2q^{13} - 4q^{17} + 4q^{19} + O(q^{20})\)  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.