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Properties

Label 185130dn
Number of curves $2$
Conductor $185130$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("dn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 185130dn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
185130.cq2 185130dn1 [1, -1, 0, 28836, 1642108] [2] 983040 \(\Gamma_0(N)\)-optimal
185130.cq1 185130dn2 [1, -1, 0, -156294, 15230650] [2] 1966080  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 185130.2.a.dn

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

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.