Properties

Label 177744bu
Number of curves $2$
Conductor $177744$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bu1")
 
E.isogeny_class()
 

Elliptic curves in class 177744bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177744.ba1 177744bu1 \([0, -1, 0, -253122973, 1550168067553]\) \(-47327266415721472000/1222082060283\) \(-46313473081586047126272\) \([]\) \(25090560\) \(3.4559\) \(\Gamma_0(N)\)-optimal
177744.ba2 177744bu2 \([0, -1, 0, -78299053, 3638812064065]\) \(-1400832679220224000/150124273180279587\) \(-5689287741624715758105047808\) \([]\) \(75271680\) \(4.0052\)  

Rank

sage: E.rank()
 

The elliptic curves in class 177744bu have rank \(0\).

Complex multiplication

The elliptic curves in class 177744bu do not have complex multiplication.

Modular form 177744.2.a.bu

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} + 3 q^{11} + 2 q^{13} + 5 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.