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Properties

Label 133518k
Number of curves $2$
Conductor $133518$
CM no
Rank $0$
Graph

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

Elliptic curves in class 133518k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
133518.cq2 133518k1 \([1, 0, 0, -117051, 24063633]\) \(-7347774183121/6119866368\) \(-147718696728379392\) \([2]\) \(3311616\) \(1.9924\) \(\Gamma_0(N)\)-optimal
133518.cq1 133518k2 \([1, 0, 0, -2151611, 1214281233]\) \(45637459887836881/13417633152\) \(323869046023087488\) \([2]\) \(6623232\) \(2.3389\)  

Rank

sage: E.rank()
 

The elliptic curves in class 133518k have rank \(0\).

Complex multiplication

The elliptic curves in class 133518k do not have complex multiplication.

Modular form 133518.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + 4 q^{5} + q^{6} - q^{7} + q^{8} + q^{9} + 4 q^{10} + q^{11} + q^{12} - 6 q^{13} - q^{14} + 4 q^{15} + q^{16} + q^{18} - 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.