Properties

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

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Show commands: SageMath
E = EllipticCurve("dp1")
 
E.isogeny_class()
 

Elliptic curves in class 98736dp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
98736.ci1 98736dp1 \([0, 1, 0, -4880, 81684]\) \(1771561/612\) \(4440864079872\) \([2]\) \(276480\) \(1.1286\) \(\Gamma_0(N)\)-optimal
98736.ci2 98736dp2 \([0, 1, 0, 14480, 585044]\) \(46268279/46818\) \(-339726102110208\) \([2]\) \(552960\) \(1.4751\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 98736.2.a.dp

sage: E.q_eigenform(10)
 
\(q + q^{3} - 4 q^{5} - 2 q^{7} + q^{9} + 6 q^{13} - 4 q^{15} + q^{17} + 4 q^{19} + O(q^{20})\) 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.