Properties

Label 115920.dc
Number of curves $4$
Conductor $115920$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("dc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 115920.dc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
115920.dc1 115920ej4 \([0, 0, 0, -434110827, 9550427546]\) \(3029968325354577848895529/1753440696000000000000\) \(5235745863204864000000000000\) \([2]\) \(53084160\) \(4.0082\)  
115920.dc2 115920ej2 \([0, 0, 0, -298633467, 1986339218474]\) \(986396822567235411402169/6336721794060000\) \(18921349889514455040000\) \([2]\) \(17694720\) \(3.4589\)  
115920.dc3 115920ej1 \([0, 0, 0, -18305787, 32287092266]\) \(-227196402372228188089/19338934824115200\) \(-57745749961850801356800\) \([2]\) \(8847360\) \(3.1124\) \(\Gamma_0(N)\)-optimal
115920.dc4 115920ej3 \([0, 0, 0, 108527253, 1193801114]\) \(47342661265381757089751/27397579603968000000\) \(-81808734336174784512000000\) \([2]\) \(26542080\) \(3.6617\)  

Rank

sage: E.rank()
 

The elliptic curves in class 115920.dc have rank \(1\).

Complex multiplication

The elliptic curves in class 115920.dc do not have complex multiplication.

Modular form 115920.2.a.dc

sage: E.q_eigenform(10)
 
\(q + q^{5} - q^{7} - 4q^{13} - 2q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.