Properties

Label 85176bn
Number of curves $2$
Conductor $85176$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bn1")
 
E.isogeny_class()
 

Elliptic curves in class 85176bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
85176.bx2 85176bn1 \([0, 0, 0, -1014, 19773]\) \(-55296/49\) \(-102173892912\) \([2]\) \(73728\) \(0.80960\) \(\Gamma_0(N)\)-optimal
85176.bx1 85176bn2 \([0, 0, 0, -18759, 988650]\) \(21882096/7\) \(233540326656\) \([2]\) \(147456\) \(1.1562\)  

Rank

sage: E.rank()
 

The elliptic curves in class 85176bn have rank \(1\).

Complex multiplication

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

Modular form 85176.2.a.bn

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