Properties

Label 16320ch
Number of curves $4$
Conductor $16320$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ch1")
 
E.isogeny_class()
 

Elliptic curves in class 16320ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16320.bm3 16320ch1 \([0, -1, 0, -6465, -172575]\) \(114013572049/15667200\) \(4107062476800\) \([2]\) \(36864\) \(1.1471\) \(\Gamma_0(N)\)-optimal
16320.bm2 16320ch2 \([0, -1, 0, -26945, 1535457]\) \(8253429989329/936360000\) \(245461155840000\) \([2, 2]\) \(73728\) \(1.4937\)  
16320.bm1 16320ch3 \([0, -1, 0, -418625, 104390625]\) \(30949975477232209/478125000\) \(125337600000000\) \([4]\) \(147456\) \(1.8403\)  
16320.bm4 16320ch4 \([0, -1, 0, 37055, 7666657]\) \(21464092074671/109596256200\) \(-28730000985292800\) \([2]\) \(147456\) \(1.8403\)  

Rank

sage: E.rank()
 

The elliptic curves in class 16320ch have rank \(0\).

Complex multiplication

The elliptic curves in class 16320ch do not have complex multiplication.

Modular form 16320.2.a.ch

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.