Properties

Label 24336by
Number of curves $3$
Conductor $24336$
CM no
Rank $1$
Graph

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

Elliptic curves in class 24336by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24336.h3 24336by1 \([0, 0, 0, 11661, 795314]\) \(12167/26\) \(-374732135571456\) \([]\) \(80640\) \(1.4807\) \(\Gamma_0(N)\)-optimal
24336.h2 24336by2 \([0, 0, 0, -110019, -27994174]\) \(-10218313/17576\) \(-253318923646304256\) \([]\) \(241920\) \(2.0300\)  
24336.h1 24336by3 \([0, 0, 0, -11182899, -14393948686]\) \(-10730978619193/6656\) \(-95931426706292736\) \([]\) \(725760\) \(2.5793\)  

Rank

sage: E.rank()
 

The elliptic curves in class 24336by have rank \(1\).

Complex multiplication

The elliptic curves in class 24336by do not have complex multiplication.

Modular form 24336.2.a.by

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.