Properties

Label 98736.u
Number of curves $2$
Conductor $98736$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("u1")
 
E.isogeny_class()
 

Elliptic curves in class 98736.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
98736.u1 98736t1 \([0, -1, 0, -22304, -1273776]\) \(676449508/561\) \(1017698018304\) \([2]\) \(215040\) \(1.2323\) \(\Gamma_0(N)\)-optimal
98736.u2 98736t2 \([0, -1, 0, -17464, -1846832]\) \(-162365474/314721\) \(-1141857176537088\) \([2]\) \(430080\) \(1.5789\)  

Rank

sage: E.rank()
 

The elliptic curves in class 98736.u have rank \(1\).

Complex multiplication

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

Modular form 98736.2.a.u

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} + 4 q^{7} + q^{9} + 4 q^{13} + 2 q^{15} + q^{17} + O(q^{20})\) 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 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.