Properties

Label 33150.bi
Number of curves $2$
Conductor $33150$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bi1")
 
E.isogeny_class()
 

Elliptic curves in class 33150.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33150.bi1 33150bl2 \([1, 1, 1, -1848763, -968312719]\) \(-71559517896165625/4598568\) \(-44907890625000\) \([]\) \(440640\) \(2.0785\)  
33150.bi2 33150bl1 \([1, 1, 1, -20638, -1600219]\) \(-99546915625/54454842\) \(-531785566406250\) \([]\) \(146880\) \(1.5292\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 33150.bi have rank \(1\).

Complex multiplication

The elliptic curves in class 33150.bi do not have complex multiplication.

Modular form 33150.2.a.bi

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} - 2 q^{7} + q^{8} + q^{9} + 3 q^{11} - q^{12} - q^{13} - 2 q^{14} + q^{16} + q^{17} + q^{18} + 2 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.