Properties

Label 84672ch
Number of curves $3$
Conductor $84672$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ch1")
 
E.isogeny_class()
 

Elliptic curves in class 84672ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
84672.t3 84672ch1 \([0, 0, 0, 4116, 71344]\) \(9261/8\) \(-6661651562496\) \([]\) \(145152\) \(1.1482\) \(\Gamma_0(N)\)-optimal
84672.t2 84672ch2 \([0, 0, 0, -42924, -4538576]\) \(-1167051/512\) \(-3837111299997696\) \([]\) \(435456\) \(1.6975\)  
84672.t1 84672ch3 \([0, 0, 0, -89964, 10520496]\) \(-132651/2\) \(-1214085997264896\) \([]\) \(435456\) \(1.6975\)  

Rank

sage: E.rank()
 

The elliptic curves in class 84672ch have rank \(0\).

Complex multiplication

The elliptic curves in class 84672ch do not have complex multiplication.

Modular form 84672.2.a.ch

sage: E.q_eigenform(10)
 
\(q - 3 q^{5} - 3 q^{11} - 4 q^{13} + 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 3 & 3 \\ 3 & 1 & 9 \\ 3 & 9 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.