Properties

Label 109200fy
Number of curves $8$
Conductor $109200$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("fy1")
 
E.isogeny_class()
 

Elliptic curves in class 109200fy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
109200.gk7 109200fy1 \([0, 1, 0, -1369408, -911396812]\) \(-4437543642183289/3033210136320\) \(-194125448724480000000\) \([2]\) \(3981312\) \(2.5933\) \(\Gamma_0(N)\)-optimal
109200.gk6 109200fy2 \([0, 1, 0, -24697408, -47240804812]\) \(26031421522845051769/5797789779600\) \(371058545894400000000\) \([2, 2]\) \(7962624\) \(2.9399\)  
109200.gk8 109200fy3 \([0, 1, 0, 11104592, 13574319188]\) \(2366200373628880151/2612420149248000\) \(-167194889551872000000000\) \([2]\) \(11943936\) \(3.1426\)  
109200.gk5 109200fy4 \([0, 1, 0, -27505408, -35834708812]\) \(35958207000163259449/12145729518877500\) \(777326689208160000000000\) \([2]\) \(15925248\) \(3.2865\)  
109200.gk3 109200fy5 \([0, 1, 0, -395137408, -3023355764812]\) \(106607603143751752938169/5290068420\) \(338564378880000000\) \([2]\) \(15925248\) \(3.2865\)  
109200.gk4 109200fy6 \([0, 1, 0, -62623408, 127262895188]\) \(424378956393532177129/136231857216000000\) \(8718838861824000000000000\) \([2, 2]\) \(23887872\) \(3.4892\)  
109200.gk1 109200fy7 \([0, 1, 0, -906271408, 10499071407188]\) \(1286229821345376481036009/247265484375000000\) \(15824991000000000000000000\) \([2]\) \(47775744\) \(3.8358\)  
109200.gk2 109200fy8 \([0, 1, 0, -398623408, -2967297104812]\) \(109454124781830273937129/3914078300576808000\) \(250501011236915712000000000\) \([2]\) \(47775744\) \(3.8358\)  

Rank

sage: E.rank()
 

The elliptic curves in class 109200fy have rank \(0\).

Complex multiplication

The elliptic curves in class 109200fy do not have complex multiplication.

Modular form 109200.2.a.fy

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} - q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.