Properties

Label 162624by
Number of curves $2$
Conductor $162624$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("by1")
 
E.isogeny_class()
 

Elliptic curves in class 162624by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162624.a2 162624by1 \([0, -1, 0, -645, -25419]\) \(-16384/147\) \(-266669534208\) \([2]\) \(268800\) \(0.87496\) \(\Gamma_0(N)\)-optimal
162624.a1 162624by2 \([0, -1, 0, -17585, -889359]\) \(20720464/63\) \(1828591091712\) \([2]\) \(537600\) \(1.2215\)  

Rank

sage: E.rank()
 

The elliptic curves in class 162624by have rank \(1\).

Complex multiplication

The elliptic curves in class 162624by do not have complex multiplication.

Modular form 162624.2.a.by

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