Properties

Label 14400.o
Number of curves 8
Conductor 14400
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("14400.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14400.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14400.o1 14400ef7 [0, 0, 0, -76802700, -259067446000] [2] 884736  
14400.o2 14400ef8 [0, 0, 0, -6530700, -874294000] [2] 884736  
14400.o3 14400ef6 [0, 0, 0, -4802700, -4043446000] [2, 2] 442368  
14400.o4 14400ef5 [0, 0, 0, -4154700, 3259514000] [2] 294912  
14400.o5 14400ef4 [0, 0, 0, -986700, -324934000] [2] 294912  
14400.o6 14400ef2 [0, 0, 0, -266700, 48026000] [2, 2] 147456  
14400.o7 14400ef3 [0, 0, 0, -194700, -108214000] [2] 221184  
14400.o8 14400ef1 [0, 0, 0, 21300, 3674000] [2] 73728 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 14400.o have rank \(1\).

Modular form 14400.2.a.o

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.