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Properties

Label 415150.l
Number of curves $1$
Conductor $415150$
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, 0, -1806692, -933374384]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([1, -1, 0, -1806692, -933374384]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([1, -1, 0, -1806692, -933374384]) 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 415150.l1 has rank \(1\).

Complex multiplication

The elliptic curves in class 415150.l do not have complex multiplication.

Modular form 415150.2.a.l

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);
 
\(q - q^{2} + q^{4} - q^{7} - q^{8} - 3 q^{9} - 3 q^{11} + 3 q^{13} + q^{14} + q^{16} - 8 q^{17} + 3 q^{18} + O(q^{20})\) 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 415150.l

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
415150.l1 415150l1 \([1, -1, 0, -1806692, -933374384]\) \(22180666338225/24117248\) \(709135737159680000\) \([]\) \(9097920\) \(2.3407\) \(\Gamma_0(N)\)-optimal