Properties

Label 283920q
Number of curves $2$
Conductor $283920$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 283920q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
283920.q1 283920q1 \([0, -1, 0, -901, -3524]\) \(1048576/525\) \(40545195600\) \([2]\) \(207360\) \(0.72826\) \(\Gamma_0(N)\)-optimal
283920.q2 283920q2 \([0, -1, 0, 3324, -30564]\) \(3286064/2205\) \(-2724637144320\) \([2]\) \(414720\) \(1.0748\)  

Rank

sage: E.rank()
 

The elliptic curves in class 283920q have rank \(0\).

Complex multiplication

The elliptic curves in class 283920q do not have complex multiplication.

Modular form 283920.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} + q^{9} + 2 q^{11} + q^{15} + 2 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.