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Properties

Label 126350ck
Number of curves $2$
Conductor $126350$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ck1")
 
E.isogeny_class()
 

Elliptic curves in class 126350ck

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
126350.dm2 126350ck1 \([1, 0, 0, 1617, -20863]\) \(397535/392\) \(-461049633800\) \([]\) \(151632\) \(0.92505\) \(\Gamma_0(N)\)-optimal
126350.dm1 126350ck2 \([1, 0, 0, -16433, 1137947]\) \(-417267265/235298\) \(-276745042688450\) \([]\) \(454896\) \(1.4744\)  

Rank

sage: E.rank()
 

The elliptic curves in class 126350ck have rank \(1\).

Complex multiplication

The elliptic curves in class 126350ck do not have complex multiplication.

Modular form 126350.2.a.ck

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} - q^{7} + q^{8} - 2 q^{9} + 3 q^{11} + q^{12} + 2 q^{13} - q^{14} + q^{16} - 3 q^{17} - 2 q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.