Properties

Label 180999s
Number of curves $2$
Conductor $180999$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 180999s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
180999.q1 180999s1 \([1, -1, 0, -71196774, -231179291641]\) \(420100556152674123/62939003491\) \(5979588098152863680577\) \([2]\) \(23224320\) \(3.1918\) \(\Gamma_0(N)\)-optimal
180999.q2 180999s2 \([1, -1, 0, -64603239, -275731807636]\) \(-313859434290315003/164114213839849\) \(-15591848383090490092166403\) \([2]\) \(46448640\) \(3.5384\)  

Rank

sage: E.rank()
 

The elliptic curves in class 180999s have rank \(1\).

Complex multiplication

The elliptic curves in class 180999s do not have complex multiplication.

Modular form 180999.2.a.s

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} - 4 q^{5} + q^{7} - 3 q^{8} - 4 q^{10} + q^{14} - q^{16} + q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.