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Properties

Label 403620.k
Number of curves $2$
Conductor $403620$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 403620.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
403620.k1 403620k1 \([0, -1, 0, -5125, -50150]\) \(1048576/525\) \(7455030920400\) \([2]\) \(711360\) \(1.1628\) \(\Gamma_0(N)\)-optimal
403620.k2 403620k2 \([0, -1, 0, 18900, -405720]\) \(3286064/2205\) \(-500978077850880\) \([2]\) \(1422720\) \(1.5094\)  

Rank

sage: E.rank()
 

The elliptic curves in class 403620.k have rank \(0\).

Complex multiplication

The elliptic curves in class 403620.k do not have complex multiplication.

Modular form 403620.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - q^{7} + q^{9} - 2 q^{11} - 4 q^{13} - q^{15} - 2 q^{17} - 2 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.