Properties

Label 152880ct
Number of curves $2$
Conductor $152880$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("ct1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 152880ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
152880.cr2 152880ct1 \([0, -1, 0, 3120, -187200]\) \(6967871/35100\) \(-16914349670400\) \([2]\) \(414720\) \(1.2205\) \(\Gamma_0(N)\)-optimal
152880.cr1 152880ct2 \([0, -1, 0, -36080, -2351040]\) \(10779215329/1232010\) \(593693673431040\) \([2]\) \(829440\) \(1.5671\)  

Rank

sage: E.rank()
 

The elliptic curves in class 152880ct have rank \(1\).

Complex multiplication

The elliptic curves in class 152880ct do not have complex multiplication.

Modular form 152880.2.a.ct

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} - 4q^{11} + q^{13} - q^{15} - 8q^{17} - 6q^{19} + O(q^{20})\)  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.