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Properties

Label 432960.n
Number of curves $1$
Conductor $432960$
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([0, -1, 0, -341, -1779]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([0, -1, 0, -341, -1779]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([0, -1, 0, -341, -1779]) 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 432960.n1 has rank \(1\).

Complex multiplication

The elliptic curves in class 432960.n do not have complex multiplication.

Modular form 432960.2.a.n

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);
 
\(q - q^{3} - q^{5} - 2 q^{7} + q^{9} + q^{11} - 4 q^{13} + q^{15} - 3 q^{17} - q^{19} + O(q^{20})\) 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 432960.n

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
432960.n1 432960n1 \([0, -1, 0, -341, -1779]\) \(268435456/60885\) \(997539840\) \([]\) \(184320\) \(0.43942\) \(\Gamma_0(N)\)-optimal