Properties

Label 13923c
Number of curves $2$
Conductor $13923$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 13923c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13923.c2 13923c1 \([1, -1, 1, -296, 2010]\) \(105890949891/1288651\) \(34793577\) \([2]\) \(3840\) \(0.25772\) \(\Gamma_0(N)\)-optimal
13923.c1 13923c2 \([1, -1, 1, -551, -1764]\) \(684030715731/338005577\) \(9126150579\) \([2]\) \(7680\) \(0.60429\)  

Rank

sage: E.rank()
 

The elliptic curves in class 13923c have rank \(2\).

Complex multiplication

The elliptic curves in class 13923c do not have complex multiplication.

Modular form 13923.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{4} - 2q^{5} + q^{7} + 3q^{8} + 2q^{10} - q^{13} - q^{14} - q^{16} - q^{17} - 8q^{19} + O(q^{20})\)  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.