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Properties

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

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 106470.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
106470.t1 106470c2 \([1, -1, 0, -3795, -89335]\) \(-1817378667/6860\) \(-22819289220\) \([]\) \(103680\) \(0.84700\)  
106470.t2 106470c1 \([1, -1, 0, 105, -675]\) \(27906957/56000\) \(-255528000\) \([]\) \(34560\) \(0.29769\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 106470.2.a.t

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} + 3 q^{11} + q^{14} + q^{16} - 6 q^{17} + q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.