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Properties

Label 424830.gc
Number of curves $1$
Conductor $424830$
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, 112160, -74127103]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([1, 1, 1, 112160, -74127103]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([1, 1, 1, 112160, -74127103]) 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 424830.gc1 has rank \(0\).

Complex multiplication

The elliptic curves in class 424830.gc do not have complex multiplication.

Modular form 424830.2.a.gc

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);
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} + 2 q^{11} - q^{12} - q^{13} - q^{15} + q^{16} + q^{18} + 5 q^{19} + O(q^{20})\) 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 424830.gc

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
424830.gc1 424830gc1 \([1, 1, 1, 112160, -74127103]\) \(4589352212399/72559411200\) \(-2467060686629683200\) \([]\) \(7318080\) \(2.2097\) \(\Gamma_0(N)\)-optimal