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Properties

Label 416025ba
Number of curves $1$
Conductor $416025$
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, 0, 1, -8043150, 8812854031]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([0, 0, 1, -8043150, 8812854031]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([0, 0, 1, -8043150, 8812854031]) 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 416025ba1 has rank \(1\).

Complex multiplication

The elliptic curves in class 416025ba do not have complex multiplication.

Modular form 416025.2.a.ba

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);
 
\(q - 2 q^{4} - 2 q^{7} + 5 q^{11} - 3 q^{13} + 4 q^{16} - 3 q^{17} - 2 q^{19} + O(q^{20})\) 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 416025ba

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
416025.ba1 416025ba1 \([0, 0, 1, -8043150, 8812854031]\) \(-799178752/3483\) \(-250790893238394421875\) \([]\) \(15138816\) \(2.7675\) \(\Gamma_0(N)\)-optimal