Properties

Label 1110.k
Number of curves $6$
Conductor $1110$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1110.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1110.k1 1110k4 \([1, 1, 1, -341005, 76503875]\) \(4385367890843575421521/24975000000\) \(24975000000\) \([4]\) \(6912\) \(1.6068\)  
1110.k2 1110k5 \([1, 1, 1, -303125, -64083373]\) \(3080272010107543650001/15465841417699560\) \(15465841417699560\) \([2]\) \(13824\) \(1.9534\)  
1110.k3 1110k3 \([1, 1, 1, -29325, 204867]\) \(2788936974993502801/1593609593601600\) \(1593609593601600\) \([2, 2]\) \(6912\) \(1.6068\)  
1110.k4 1110k2 \([1, 1, 1, -21325, 1187267]\) \(1072487167529950801/2554882560000\) \(2554882560000\) \([2, 4]\) \(3456\) \(1.2602\)  
1110.k5 1110k1 \([1, 1, 1, -845, 32195]\) \(-66730743078481/419010969600\) \(-419010969600\) \([4]\) \(1728\) \(0.91367\) \(\Gamma_0(N)\)-optimal
1110.k6 1110k6 \([1, 1, 1, 116475, 1779507]\) \(174751791402194852399/102423900876336360\) \(-102423900876336360\) \([2]\) \(13824\) \(1.9534\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1110.k have rank \(0\).

Complex multiplication

The elliptic curves in class 1110.k do not have complex multiplication.

Modular form 1110.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} + 4q^{11} - q^{12} - 2q^{13} - q^{15} + q^{16} + 2q^{17} + q^{18} + 4q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.