Properties

Label 14400bt
Number of curves $4$
Conductor $14400$
CM no
Rank $2$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14400bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.f3 14400bt1 \([0, 0, 0, -975, -11500]\) \(140608/3\) \(2187000000\) \([2]\) \(8192\) \(0.58123\) \(\Gamma_0(N)\)-optimal
14400.f2 14400bt2 \([0, 0, 0, -2100, 20000]\) \(21952/9\) \(419904000000\) \([2, 2]\) \(16384\) \(0.92780\)  
14400.f1 14400bt3 \([0, 0, 0, -29100, 1910000]\) \(7301384/3\) \(1119744000000\) \([2]\) \(32768\) \(1.2744\)  
14400.f4 14400bt4 \([0, 0, 0, 6900, 146000]\) \(97336/81\) \(-30233088000000\) \([2]\) \(32768\) \(1.2744\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14400bt have rank \(2\).

Complex multiplication

The elliptic curves in class 14400bt do not have complex multiplication.

Modular form 14400.2.a.bt

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