Properties

Label 72450dc
Number of curves $2$
Conductor $72450$
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 72450dc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
72450.ei2 72450dc1 \([1, -1, 1, -170, 25257]\) \(-160103007/81288256\) \(-274347864000\) \([2]\) \(73728\) \(0.87390\) \(\Gamma_0(N)\)-optimal
72450.ei1 72450dc2 \([1, -1, 1, -13970, 632457]\) \(89332607016927/1060723384\) \(3579941421000\) \([2]\) \(147456\) \(1.2205\)  

Rank

sage: E.rank()
 

The elliptic curves in class 72450dc have rank \(1\).

Complex multiplication

The elliptic curves in class 72450dc do not have complex multiplication.

Modular form 72450.2.a.dc

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