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Properties

Label 503963.a
Number of curves $1$
Conductor $503963$
CM no
Rank $0$
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, -132, -550]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([1, -1, 1, -132, -550]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([1, -1, 1, -132, -550]) 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 503963.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 503963.a do not have complex multiplication.

Modular form 503963.2.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);
 
\(q - q^{2} - q^{4} - 4 q^{5} + 4 q^{7} + 3 q^{8} - 3 q^{9} + 4 q^{10} - 4 q^{14} - q^{16} - 7 q^{17} + 3 q^{18} - 2 q^{19} + O(q^{20})\) 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 503963.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
503963.a1 \([1, -1, 1, -132, -550]\) \(-252555814161/503963\) \(-503963\) \([]\) \(126428\) \(-0.018213\)