↑

Properties

Label 72450w
Number of curves $2$
Conductor $72450$
CM no
Rank $2$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 72450w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
72450.u1 72450w1 [1, -1, 0, -5292, -80384] [2] 147456 \(\Gamma_0(N)\)-optimal
72450.u2 72450w2 [1, -1, 0, 17208, -597884] [2] 294912  

Rank

sage: E.rank()
 

The elliptic curves in class 72450w have rank \(2\).

Complex multiplication

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

Modular form 72450.2.a.w

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

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.