Properties

Label 156816by
Number of curves $2$
Conductor $156816$
CM no
Rank $1$
Graph

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

Elliptic curves in class 156816by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
156816.db2 156816by1 \([0, 0, 0, 8349, 29282]\) \(109503/64\) \(-37616731029504\) \([]\) \(414720\) \(1.2943\) \(\Gamma_0(N)\)-optimal
156816.db1 156816by2 \([0, 0, 0, -107811, -14877918]\) \(-35937/4\) \(-15425210767785984\) \([]\) \(1244160\) \(1.8436\)  

Rank

sage: E.rank()
 

The elliptic curves in class 156816by have rank \(1\).

Complex multiplication

The elliptic curves in class 156816by do not have complex multiplication.

Modular form 156816.2.a.by

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.