Properties

Label 2093.d
Number of curves $2$
Conductor $2093$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2093.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2093.d1 2093d2 \([1, 1, 1, -98, -296]\) \(104154702625/32188247\) \(32188247\) \([2]\) \(480\) \(0.14515\)  
2093.d2 2093d1 \([1, 1, 1, 17, -20]\) \(541343375/625807\) \(-625807\) \([2]\) \(240\) \(-0.20142\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2093.d have rank \(0\).

Complex multiplication

The elliptic curves in class 2093.d do not have complex multiplication.

Modular form 2093.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} + 2 q^{3} - q^{4} - 2 q^{6} + q^{7} + 3 q^{8} + q^{9} - 4 q^{11} - 2 q^{12} - q^{13} - q^{14} - q^{16} + 8 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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 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.