↑

Properties

Label 480249bq
Number of curves $2$
Conductor $480249$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath
Copy content comment:Define the isogeny class
 
Copy content sage:E = EllipticCurve([1, -1, 0, -490254, 126853271]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([1, -1, 0, -490254, 126853271]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([1, -1, 0, -490254, 126853271]) ellisomat(E)
 

Rank

Copy content comment:Mordell-Weil rank
 
Copy content sage:E.rank()
 
Copy content gp:[lower,upper] = ellrank(E)
 
Copy content magma:Rank(E);
 

The elliptic curves in class 480249bq have rank \(1\).

Complex multiplication

The elliptic curves in class 480249bq do not have complex multiplication.

Modular form 480249.2.a.bq

Copy content comment:q-expansion of modular form
 
Copy content sage:E.q_eigenform(20)
 
Copy content gp:Ser(ellan(E,20),q)*q
 
Copy content magma:ModularForm(E);
 
\(q + q^{2} - q^{4} + q^{5} - 3 q^{8} + q^{10} + 5 q^{13} - q^{16} + 3 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content comment:Isogeny matrix
 
Copy content sage:E.isogeny_class().matrix()
 
Copy content gp:ellisomat(E)
 

The \((i,j)\)-th 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

Copy content comment:Isogeny graph
 
Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 480249bq

Copy content comment:List of curves in the isogeny class
 
Copy content sage:E.isogeny_class().curves
 
Copy content magma:IsogenousCurves(E);
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
480249.bq2 480249bq1 \([1, -1, 0, -490254, 126853271]\) \(21609\) \(603049522971892689\) \([]\) \(4498200\) \(2.1731\) \(\Gamma_0(N)\)-optimal
480249.bq1 480249bq2 \([1, -1, 0, -185386119, -971500917304]\) \(1168429123449\) \(603049522971892689\) \([]\) \(31487400\) \(3.1461\)