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Properties

Label 106470d
Number of curves $2$
Conductor $106470$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 106470d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
106470.g2 106470d1 \([1, -1, 0, -2625, -46539]\) \(438484480083/42875000\) \(195638625000\) \([]\) \(124416\) \(0.90367\) \(\Gamma_0(N)\)-optimal
106470.g1 106470d2 \([1, -1, 0, -207375, -36296389]\) \(296494123539627/350\) \(1164249450\) \([]\) \(373248\) \(1.4530\)  

Rank

sage: E.rank()
 

The elliptic curves in class 106470d have rank \(1\).

Complex multiplication

The elliptic curves in class 106470d do not have complex multiplication.

Modular form 106470.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} - 3 q^{11} + q^{14} + q^{16} + 3 q^{17} + q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.