↑

Properties

Label 443760dc
Number of curves $2$
Conductor $443760$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 443760dc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
443760.dc2 443760dc1 \([0, 1, 0, 2480, 18068]\) \(222641831/145800\) \(-1104216883200\) \([]\) \(580608\) \(0.99969\) \(\Gamma_0(N)\)-optimal
443760.dc1 443760dc2 \([0, 1, 0, -28480, -2173900]\) \(-337335507529/72000000\) \(-545292288000000\) \([]\) \(1741824\) \(1.5490\)  

Rank

sage: E.rank()
 

The elliptic curves in class 443760dc have rank \(1\).

Complex multiplication

The elliptic curves in class 443760dc do not have complex multiplication.

Modular form 443760.2.a.dc

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + 2 q^{7} + q^{9} + 3 q^{11} - 4 q^{13} + q^{15} - 3 q^{17} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.