Properties

Label 405720.gm
Number of curves $2$
Conductor $405720$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("gm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 405720.gm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
405720.gm1 405720gm1 \([0, 0, 0, -38367, -796446]\) \(10536048/5635\) \(3340514938763520\) \([2]\) \(2211840\) \(1.6700\) \(\Gamma_0(N)\)-optimal
405720.gm2 405720gm2 \([0, 0, 0, 146853, -6241914]\) \(147704148/92575\) \(-219519553118745600\) \([2]\) \(4423680\) \(2.0166\)  

Rank

sage: E.rank()
 

The elliptic curves in class 405720.gm have rank \(0\).

Complex multiplication

The elliptic curves in class 405720.gm do not have complex multiplication.

Modular form 405720.2.a.gm

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