Properties

Label 98736cu
Number of curves $2$
Conductor $98736$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("cu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 98736cu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
98736.ce1 98736cu1 [0, -1, 0, -379496, -89799312] [2] 1105920 \(\Gamma_0(N)\)-optimal
98736.ce2 98736cu2 [0, -1, 0, -302056, -127590032] [2] 2211840  

Rank

sage: E.rank()
 

The elliptic curves in class 98736cu have rank \(0\).

Complex multiplication

The elliptic curves in class 98736cu do not have complex multiplication.

Modular form 98736.2.a.cu

sage: E.q_eigenform(10)
 
\( q - q^{3} + 4q^{5} - 2q^{7} + q^{9} - 4q^{15} + q^{17} + O(q^{20}) \)

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.