Show commands: Magma / Pari/GP / SageMath
Copy content comment:Define the isogeny class
 
Copy content sage:E = EllipticCurve([0, 1, 0, -2008, 115988]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([0, 1, 0, -2008, 115988]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([0, 1, 0, -2008, 115988]) 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 418800.bu1 has rank \(1\).

Complex multiplication

The elliptic curves in class 418800.bu do not have complex multiplication.

Modular form 418800.2.a.bu

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);
 
\(q + q^{3} + q^{7} + q^{9} - 4 q^{11} + 3 q^{13} - 3 q^{17} + 3 q^{19} + O(q^{20})\) 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 418800.bu

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
418800.bu1 418800bu1 \([0, 1, 0, -2008, 115988]\) \(-13997521/83760\) \(-5360640000000\) \([]\) \(663552\) \(1.1262\) \(\Gamma_0(N)\)-optimal