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Properties

Label 80223.d
Number of curves $2$
Conductor $80223$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 80223.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
80223.d1 80223d1 \([1, 1, 1, -13373, 584090]\) \(149298747625/1611753\) \(2855318756433\) \([2]\) \(184320\) \(1.2054\) \(\Gamma_0(N)\)-optimal
80223.d2 80223d2 \([1, 1, 1, -3088, 1472714]\) \(-1838265625/528749793\) \(-936712512036873\) \([2]\) \(368640\) \(1.5520\)  

Rank

sage: E.rank()
 

The elliptic curves in class 80223.d have rank \(0\).

Complex multiplication

The elliptic curves in class 80223.d do not have complex multiplication.

Modular form 80223.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} + q^{6} + 4 q^{7} + 3 q^{8} + q^{9} + q^{12} - q^{13} - 4 q^{14} - q^{16} - q^{17} - q^{18} + 2 q^{19} + O(q^{20})\) 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 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.