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Properties

Label 188442f
Number of curves $2$
Conductor $188442$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 188442f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
188442.bn2 188442f1 \([1, -1, 1, 16177, 1311383]\) \(13651919/29696\) \(-1018467297506304\) \([]\) \(864000\) \(1.5640\) \(\Gamma_0(N)\)-optimal
188442.bn1 188442f2 \([1, -1, 1, -1478363, -696183937]\) \(-10418796526321/82044596\) \(-2813838158779516404\) \([]\) \(4320000\) \(2.3687\)  

Rank

sage: E.rank()
 

The elliptic curves in class 188442f have rank \(2\).

Complex multiplication

The elliptic curves in class 188442f do not have complex multiplication.

Modular form 188442.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - 2 q^{7} + q^{8} - q^{10} + 3 q^{11} + q^{13} - 2 q^{14} + q^{16} - 8 q^{17} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.