Show commands: Magma / Pari/GP / SageMath
Copy content comment:Define the isogeny class
 
Copy content sage:E = EllipticCurve([0, 1, 1, -228, 1248]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([0, 1, 1, -228, 1248]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([0, 1, 1, -228, 1248]) 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 4225973.a1 has rank \(4\).

Complex multiplication

The elliptic curves in class 4225973.a do not have complex multiplication.

Modular form 4225973.2.a.a

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);
 
\(q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 4 q^{6} - 4 q^{7} + q^{9} - 5 q^{11} - 4 q^{12} - 2 q^{13} + 8 q^{14} - 4 q^{16} - 6 q^{17} - 2 q^{18} - 6 q^{19} + O(q^{20})\) 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 4225973.a

Copy content comment:List of curves in the isogeny class
 
Copy content sage:E.isogeny_class().curves
 
Copy content magma:IsogenousCurves(E);
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
4225973.a1 \([0, 1, 1, -228, 1248]\) \(1316532736000/4225973\) \(4225973\) \([]\) \(2346800\) \(0.13767\)