Properties

Label 101150l
Number of curves $2$
Conductor $101150$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 101150l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
101150.j1 101150l1 \([1, 1, 0, -50725, 4377125]\) \(-11060825617/2744\) \(-3580962875000\) \([]\) \(326592\) \(1.3965\) \(\Gamma_0(N)\)-optimal
101150.j2 101150l2 \([1, 1, 0, 21525, 15575875]\) \(845095823/80707214\) \(-105324175320218750\) \([]\) \(979776\) \(1.9458\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 101150.2.a.l

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.