Properties

Label 187200.qg
Number of curves $2$
Conductor $187200$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("qg1")
 
E.isogeny_class()
 

Elliptic curves in class 187200.qg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187200.qg1 187200kn2 \([0, 0, 0, -163159500, 802170470000]\) \(-6434774386429585/140608\) \(-10496330956800000000\) \([]\) \(24883200\) \(3.1761\)  
187200.qg2 187200kn1 \([0, 0, 0, -1879500, 1253990000]\) \(-9836106385/3407872\) \(-254396281651200000000\) \([]\) \(8294400\) \(2.6268\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 187200.qg have rank \(1\).

Complex multiplication

The elliptic curves in class 187200.qg do not have complex multiplication.

Modular form 187200.2.a.qg

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