Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("bi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 85176.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
85176.bi1 85176bp2 \([0, 0, 0, -1755, 28054]\) \(4920750/49\) \(5952780288\) \([2]\) \(52224\) \(0.69422\)  
85176.bi2 85176bp1 \([0, 0, 0, -195, -338]\) \(13500/7\) \(425198592\) \([2]\) \(26112\) \(0.34765\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 85176.2.a.bi

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