Properties

Label 179520da
Number of curves $2$
Conductor $179520$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("da1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 179520da

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
179520.dy2 179520da1 [0, -1, 0, 1695, -24063] [2] 196608 \(\Gamma_0(N)\)-optimal
179520.dy1 179520da2 [0, -1, 0, -9185, -213375] [2] 393216  

Rank

sage: E.rank()
 

The elliptic curves in class 179520da have rank \(1\).

Complex multiplication

The elliptic curves in class 179520da do not have complex multiplication.

Modular form 179520.2.a.da

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{5} + 2q^{7} + q^{9} + q^{11} - q^{15} + q^{17} + O(q^{20}) \)

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.