Properties

Label 439824dc
Number of curves $2$
Conductor $439824$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("dc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 439824dc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
439824.dc1 439824dc1 [0, 1, 0, -153680, -23225196] [2] 3317760 \(\Gamma_0(N)\)-optimal
439824.dc2 439824dc2 [0, 1, 0, -122320, -32946796] [2] 6635520  

Rank

sage: E.rank()
 

The elliptic curves in class 439824dc have rank \(1\).

Complex multiplication

The elliptic curves in class 439824dc do not have complex multiplication.

Modular form 439824.2.a.dc

sage: E.q_eigenform(10)
 
\( q + q^{3} - 4q^{5} + q^{9} - q^{11} - 4q^{15} + q^{17} + O(q^{20}) \)

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.