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Properties

Label 405720s
Number of curves $1$
Conductor $405720$
CM no
Rank $2$
Graph

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Show commands: Magma / Pari/GP / SageMath
Copy content comment:Define the isogeny class
 
Copy content sage:E = EllipticCurve([0, 0, 0, -68943, -3066077]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([0, 0, 0, -68943, -3066077]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([0, 0, 0, -68943, -3066077]) 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 405720s1 has rank \(2\).

Complex multiplication

The elliptic curves in class 405720s do not have complex multiplication.

Modular form 405720.2.a.s

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);
 
\(q - q^{5} - 3 q^{11} - 4 q^{13} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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 405720s

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
405720.s1 405720s1 \([0, 0, 0, -68943, -3066077]\) \(538967296/251505\) \(16911356877490320\) \([]\) \(2107392\) \(1.8083\) \(\Gamma_0(N)\)-optimal