Properties

Label 16800i
Number of curves $4$
Conductor $16800$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 16800i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16800.z3 16800i1 \([0, -1, 0, -159468758, -775053481488]\) \(448487713888272974160064/91549016015625\) \(91549016015625000000\) \([2, 2]\) \(2580480\) \(3.2181\) \(\Gamma_0(N)\)-optimal
16800.z1 16800i2 \([0, -1, 0, -2551500008, -49605979418988]\) \(229625675762164624948320008/9568125\) \(76545000000000\) \([2]\) \(5160960\) \(3.5647\)  
16800.z2 16800i3 \([0, -1, 0, -160015633, -769469340863]\) \(7079962908642659949376/100085966990454375\) \(6405501887389080000000000\) \([2]\) \(5160960\) \(3.5647\)  
16800.z4 16800i4 \([0, -1, 0, -158922008, -780632518488]\) \(-55486311952875723077768/801237030029296875\) \(-6409896240234375000000000\) \([2]\) \(5160960\) \(3.5647\)  

Rank

sage: E.rank()
 

The elliptic curves in class 16800i have rank \(0\).

Complex multiplication

The elliptic curves in class 16800i do not have complex multiplication.

Modular form 16800.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} + q^{9} + 4q^{11} + 6q^{13} - 6q^{17} + 4q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.