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Properties

Label 442090d
Number of curves $1$
Conductor $442090$
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, 1, -3995, 104937]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([1, 1, 1, -3995, 104937]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([1, 1, 1, -3995, 104937]) 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 442090d1 has rank \(1\).

Complex multiplication

The elliptic curves in class 442090d do not have complex multiplication.

Modular form 442090.2.a.d

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);
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{7} + q^{8} - 2 q^{9} + q^{10} + q^{11} - q^{12} - 4 q^{13} + q^{14} - q^{15} + q^{16} - 4 q^{17} - 2 q^{18} - 7 q^{19} + O(q^{20})\) 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 442090d

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
442090.d1 442090d1 \([1, 1, 1, -3995, 104937]\) \(-7051489400044081/828497880320\) \(-828497880320\) \([]\) \(752640\) \(1.0228\) \(\Gamma_0(N)\)-optimal