Properties

Label 182070.ci
Number of curves $2$
Conductor $182070$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ci1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 182070.ci

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
182070.ci1 182070bn2 \([1, -1, 1, -1348673, -443775463]\) \(15417797707369/4080067320\) \(71794038810174763320\) \([2]\) \(5308416\) \(2.5186\)  
182070.ci2 182070bn1 \([1, -1, 1, 211927, -44886103]\) \(59822347031/83966400\) \(-1477496940013886400\) \([2]\) \(2654208\) \(2.1720\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 182070.ci have rank \(1\).

Complex multiplication

The elliptic curves in class 182070.ci do not have complex multiplication.

Modular form 182070.2.a.ci

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - q^{10} + 2q^{11} - 2q^{13} - q^{14} + q^{16} - 4q^{19} + O(q^{20})\)  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.