↑

Properties

Label 454854h
Number of curves $1$
Conductor $454854$
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, 0, 1, -876465, 668049220]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([1, 0, 1, -876465, 668049220]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([1, 0, 1, -876465, 668049220]) 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 454854h1 has rank \(1\).

Complex multiplication

The elliptic curves in class 454854h do not have complex multiplication.

Modular form 454854.2.a.h

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);
 
\(q - q^{2} + q^{3} + q^{4} - 3 q^{5} - q^{6} - q^{8} + q^{9} + 3 q^{10} - 5 q^{11} + q^{12} - q^{13} - 3 q^{15} + q^{16} - q^{18} + O(q^{20})\) 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 454854h

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
454854.h1 454854h1 \([1, 0, 1, -876465, 668049220]\) \(-11779205551777/23689304064\) \(-149748691366695131136\) \([]\) \(18213888\) \(2.5607\) \(\Gamma_0(N)\)-optimal