Properties

Label 85176.bo
Number of curves $2$
Conductor $85176$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 85176.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
85176.bo1 85176bg1 \([0, 0, 0, -9796254, -11801526035]\) \(49860882714802176/57967\) \(120871715314896\) \([2]\) \(1290240\) \(2.4165\) \(\Gamma_0(N)\)-optimal
85176.bo2 85176bg2 \([0, 0, 0, -9793719, -11807939078]\) \(-3113886554501616/3360173089\) \(-112105131546537222912\) \([2]\) \(2580480\) \(2.7631\)  

Rank

sage: E.rank()
 

The elliptic curves in class 85176.bo have rank \(0\).

Complex multiplication

The elliptic curves in class 85176.bo do not have complex multiplication.

Modular form 85176.2.a.bo

sage: E.q_eigenform(10)
 
\(q + 2q^{5} - q^{7} - 2q^{11} + 6q^{17} - 4q^{19} + O(q^{20})\)  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.