Properties

Label 154560.dx
Number of curves $2$
Conductor $154560$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("dx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 154560.dx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
154560.dx1 154560gm1 \([0, -1, 0, -1505, 12897]\) \(1439069689/579600\) \(151938662400\) \([2]\) \(147456\) \(0.84352\) \(\Gamma_0(N)\)-optimal
154560.dx2 154560gm2 \([0, -1, 0, 4895, 88417]\) \(49471280711/41992020\) \(-11007956090880\) \([2]\) \(294912\) \(1.1901\)  

Rank

sage: E.rank()
 

The elliptic curves in class 154560.dx have rank \(1\).

Complex multiplication

The elliptic curves in class 154560.dx do not have complex multiplication.

Modular form 154560.2.a.dx

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{7} + q^{9} + 2q^{11} - 4q^{13} - q^{15} - 6q^{17} + 4q^{19} + O(q^{20})\)  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 LMFDB 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 LMFDB labels.