Properties

Label 14400bo
Number of curves 8
Conductor 14400
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("14400.ez1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14400bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.ez8 14400bo1 [0, 0, 0, 21300, -3674000] [2] 73728 \(\Gamma_0(N)\)-optimal
14400.ez6 14400bo2 [0, 0, 0, -266700, -48026000] [2, 2] 147456  
14400.ez7 14400bo3 [0, 0, 0, -194700, 108214000] [2] 221184  
14400.ez4 14400bo4 [0, 0, 0, -4154700, -3259514000] [2] 294912  
14400.ez5 14400bo5 [0, 0, 0, -986700, 324934000] [2] 294912  
14400.ez3 14400bo6 [0, 0, 0, -4802700, 4043446000] [2, 2] 442368  
14400.ez2 14400bo7 [0, 0, 0, -6530700, 874294000] [2] 884736  
14400.ez1 14400bo8 [0, 0, 0, -76802700, 259067446000] [2] 884736  

Rank

sage: E.rank()
 

The elliptic curves in class 14400bo have rank \(0\).

Modular form 14400.2.a.ez

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

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.