↑

Properties

Label 446490.q
Number of curves $1$
Conductor $446490$
CM no
Rank $2$
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, 8145, 27121]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([1, -1, 0, 8145, 27121]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([1, -1, 0, 8145, 27121]) 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 curve 446490.q1 has rank \(2\).

Complex multiplication

The elliptic curves in class 446490.q do not have complex multiplication.

Modular form 446490.2.a.q

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);
 
\(q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} - 4 q^{13} + q^{14} + q^{16} - 5 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny graph

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

Elliptic curves in class 446490.q

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
446490.q1 446490q1 \([1, -1, 0, 8145, 27121]\) \(46268279/27060\) \(-34947123241140\) \([]\) \(1136640\) \(1.2882\) \(\Gamma_0(N)\)-optimal