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Properties

Label 185130ch
Number of curves $2$
Conductor $185130$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("ch1")
 
E.isogeny_class()
 

Elliptic curves in class 185130ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
185130.do2 185130ch1 \([1, -1, 1, -18173, 2056321]\) \(-19034163/41140\) \(-1434536790605820\) \([2]\) \(1105920\) \(1.5972\) \(\Gamma_0(N)\)-optimal
185130.do1 185130ch2 \([1, -1, 1, -377543, 89311357]\) \(170676802323/158950\) \(5542528509158850\) \([2]\) \(2211840\) \(1.9437\)  

Rank

sage: E.rank()
 

The elliptic curves in class 185130ch have rank \(1\).

Complex multiplication

The elliptic curves in class 185130ch do not have complex multiplication.

Modular form 185130.2.a.ch

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} - 6 q^{13} + q^{16} - q^{17} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.