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Properties

Label 462462u
Number of curves $1$
Conductor $462462$
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([1, 1, 0, -321322278, -2105880818796]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([1, 1, 0, -321322278, -2105880818796]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([1, 1, 0, -321322278, -2105880818796]) 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 462462u1 has rank \(2\).

Complex multiplication

The elliptic curves in class 462462u do not have complex multiplication.

Modular form 462462.2.a.u

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);
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} + q^{9} + q^{10} - q^{12} + q^{13} + q^{15} + q^{16} - 3 q^{17} - q^{18} - 3 q^{19} + O(q^{20})\) 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 462462u

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
462462.u1 462462u1 \([1, 1, 0, -321322278, -2105880818796]\) \(7331784894054481/415039832064\) \(207695118702873087434244096\) \([]\) \(186278400\) \(3.8044\) \(\Gamma_0(N)\)-optimal