Properties

Label 101150o
Number of curves $4$
Conductor $101150$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 101150o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101150.w3 101150o1 \([1, -1, 0, -135017, 18822141]\) \(721734273/13328\) \(5026648744250000\) \([2]\) \(589824\) \(1.8073\) \(\Gamma_0(N)\)-optimal
101150.w2 101150o2 \([1, -1, 0, -279517, -28429359]\) \(6403769793/2775556\) \(1046799600990062500\) \([2, 2]\) \(1179648\) \(2.1539\)  
101150.w4 101150o3 \([1, -1, 0, 948733, -211438609]\) \(250404380127/196003234\) \(-73922524764033531250\) \([2]\) \(2359296\) \(2.5005\)  
101150.w1 101150o4 \([1, -1, 0, -3819767, -2871250109]\) \(16342588257633/8185058\) \(3086990660062531250\) \([2]\) \(2359296\) \(2.5005\)  

Rank

sage: E.rank()
 

The elliptic curves in class 101150o have rank \(0\).

Complex multiplication

The elliptic curves in class 101150o do not have complex multiplication.

Modular form 101150.2.a.o

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.