Properties

Label 176400fm
Number of curves $8$
Conductor $176400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("176400.lm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 176400fm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176400.lm7 176400fm1 [0, 0, 0, -7236075, 2636212250] [2] 10616832 \(\Gamma_0(N)\)-optimal
176400.lm5 176400fm2 [0, 0, 0, -63684075, -193746379750] [2, 2] 21233664  
176400.lm4 176400fm3 [0, 0, 0, -472932075, 3958639060250] [2] 31850496  
176400.lm6 176400fm4 [0, 0, 0, -14292075, -486591547750] [2] 42467328  
176400.lm2 176400fm5 [0, 0, 0, -1016244075, -12469387099750] [2] 42467328  
176400.lm3 176400fm6 [0, 0, 0, -476460075, 3896578012250] [2, 2] 63700992  
176400.lm8 176400fm7 [0, 0, 0, 128591925, 13116965440250] [2] 127401984  
176400.lm1 176400fm8 [0, 0, 0, -1137960075, -9295716487750] [2] 127401984  

Rank

sage: E.rank()
 

The elliptic curves in class 176400fm have rank \(0\).

Modular form 176400.2.a.lm

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

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.