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Properties

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

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Show commands: Magma / Pari/GP / SageMath
Copy content comment:Define the isogeny class
 
Copy content sage:E = EllipticCurve([1, -1, 1, -36686, 7071166]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([1, -1, 1, -36686, 7071166]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([1, -1, 1, -36686, 7071166]) 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 480249f1 has rank \(1\).

Complex multiplication

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

Modular form 480249.2.a.f

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);
 
\(q - q^{2} - q^{4} - 2 q^{5} + 3 q^{8} + 2 q^{10} - q^{13} - q^{16} - 2 q^{17} + O(q^{20})\) 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 480249f

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.f1 480249f1 \([1, -1, 1, -36686, 7071166]\) \(-297\) \(-18384729725270601\) \([]\) \(2566080\) \(1.8070\) \(\Gamma_0(N)\)-optimal